Practica6: Combinaciones y Permutaciones mediante R

19041220 JESUS ALBERTO LOPEZ ALDANA
19041192 ALEXEI GUADALUPE BRISEÑO PUGA
19041234 CAROLINA ORTIZ SIMENTAL
19041226 ABRAHAM IGNACIO MARTINEZ CASTILLO
19041223 JAZHIEL MARQUEZ SOLIS

Importar la libreria

library(gtools)

Los datos y datos ordenados

nombres <- c("Jesus", "Alexei", "Luis", "Abraham", "Caro", "Jazhiel", "Paty", "Adriana", "Olga", "Mary")

nombres <- sort(nombres)

nombres

##  [1] "Abraham" "Adriana" "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Luis"   
##  [8] "Mary"    "Olga"    "Paty"

Combinaciones en grupos de 2

N <- length(nombres) # Cantidad de alumnos
n <- 2 # Grupos de 2 

combinaciones <- combinations(N, n, nombres)

head(combinaciones)

##      [,1]      [,2]     
## [1,] "Abraham" "Adriana"
## [2,] "Abraham" "Alexei" 
## [3,] "Abraham" "Caro"   
## [4,] "Abraham" "Jazhiel"
## [5,] "Abraham" "Jesus"  
## [6,] "Abraham" "Luis"

¿Cuantas combinaciones salen?

nrow(combinaciones)

## [1] 45

Comprobacion conforme a la formula

factorial(N) / (factorial(n) * (factorial (N-n)))

## [1] 45

Permutaciones con grupos de 2

N <- length(nombres) 
n <- 2 

permutaciones <- permutations(N, n, nombres)

head(permutaciones)

##      [,1]      [,2]     
## [1,] "Abraham" "Adriana"
## [2,] "Abraham" "Alexei" 
## [3,] "Abraham" "Caro"   
## [4,] "Abraham" "Jazhiel"
## [5,] "Abraham" "Jesus"  
## [6,] "Abraham" "Luis"

¿Cuantas permutaciones salen?

nrow(permutaciones)

## [1] 90

Comprobar mediante la formula

factorial(N) / (factorial (N-n))

## [1] 90

Combinaciones grupos de 4

N <- length(nombres) # Cantidad de alumnos
n <- 4 # Grupos de 4 

combinaciones <- combinations(N, n, nombres)

head(combinaciones)

##      [,1]      [,2]      [,3]     [,4]     
## [1,] "Abraham" "Adriana" "Alexei" "Caro"   
## [2,] "Abraham" "Adriana" "Alexei" "Jazhiel"
## [3,] "Abraham" "Adriana" "Alexei" "Jesus"  
## [4,] "Abraham" "Adriana" "Alexei" "Luis"   
## [5,] "Abraham" "Adriana" "Alexei" "Mary"   
## [6,] "Abraham" "Adriana" "Alexei" "Olga"

####¿Cuantas combinaciones salen?

nrow(combinaciones)

## [1] 210

Comprobar mediante la formula

factorial(N) / (factorial(n) * (factorial (N-n)))

## [1] 210

permutaciones con grupos de 4

N <- length(nombres) 
n <- 4 

permutaciones <- permutations(N, n, nombres)

head(permutaciones)

##      [,1]      [,2]      [,3]     [,4]     
## [1,] "Abraham" "Adriana" "Alexei" "Caro"   
## [2,] "Abraham" "Adriana" "Alexei" "Jazhiel"
## [3,] "Abraham" "Adriana" "Alexei" "Jesus"  
## [4,] "Abraham" "Adriana" "Alexei" "Luis"   
## [5,] "Abraham" "Adriana" "Alexei" "Mary"   
## [6,] "Abraham" "Adriana" "Alexei" "Olga"

¿Cuantas permutaciones salen?

nrow(permutaciones)

## [1] 5040

Comprobar mediante la formula

factorial(N) / (factorial (N-n))

## [1] 5040

Combinaciones con grupos de 6

N <- length(nombres) 
n <- 6 

combinaciones <- combinations(N, n, nombres)

head(combinaciones)

##      [,1]      [,2]      [,3]     [,4]   [,5]      [,6]   
## [1,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Jesus"
## [2,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Luis" 
## [3,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Mary" 
## [4,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Olga" 
## [5,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Paty" 
## [6,] "Abraham" "Adriana" "Alexei" "Caro" "Jesus"   "Luis"

¿Cuantas combinaciones salen?

nrow(combinaciones)

## [1] 210

Comprobacion mediante la formula

factorial(N) / (factorial(n) * (factorial (N-n)))

## [1] 210

Permutaciones con grupos de 6

N <- length(nombres)
n <- 6 

permutaciones <- permutations(N, n, nombres)

head(permutaciones)

##      [,1]      [,2]      [,3]     [,4]   [,5]      [,6]     
## [1,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Jesus"  
## [2,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Luis"   
## [3,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Mary"   
## [4,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Olga"   
## [5,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Paty"   
## [6,] "Abraham" "Adriana" "Alexei" "Caro" "Jesus"   "Jazhiel"

####¿Cuantas permutaciones salen?

nrow(permutaciones)

## [1] 151200

Comprobar conforme a la fórmula

factorial(N) / (factorial (N-n))

## [1] 151200

Analizando datos con COMBINACIONES de grupos de 6

Pregunta 9 ¿En cuántas combinaciones de grupos seis está ‘Adriana’ en la primera columna?.

combinaciones[which(combinaciones[,1] == 'Adriana'),]

##       [,1]      [,2]      [,3]      [,4]      [,5]    [,6]  
##  [1,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Jesus" "Luis"
##  [2,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Jesus" "Mary"
##  [3,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Jesus" "Olga"
##  [4,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Jesus" "Paty"
##  [5,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Luis"  "Mary"
##  [6,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Luis"  "Olga"
##  [7,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Luis"  "Paty"
##  [8,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Mary"  "Olga"
##  [9,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Mary"  "Paty"
## [10,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Olga"  "Paty"
## [11,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Luis"  "Mary"
## [12,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Luis"  "Olga"
## [13,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Luis"  "Paty"
## [14,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Mary"  "Olga"
## [15,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Mary"  "Paty"
## [16,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Olga"  "Paty"
## [17,] "Adriana" "Alexei"  "Caro"    "Luis"    "Mary"  "Olga"
## [18,] "Adriana" "Alexei"  "Caro"    "Luis"    "Mary"  "Paty"
## [19,] "Adriana" "Alexei"  "Caro"    "Luis"    "Olga"  "Paty"
## [20,] "Adriana" "Alexei"  "Caro"    "Mary"    "Olga"  "Paty"
## [21,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Luis"  "Mary"
## [22,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Luis"  "Olga"
## [23,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Luis"  "Paty"
## [24,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Mary"  "Olga"
## [25,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Mary"  "Paty"
## [26,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Olga"  "Paty"
## [27,] "Adriana" "Alexei"  "Jazhiel" "Luis"    "Mary"  "Olga"
## [28,] "Adriana" "Alexei"  "Jazhiel" "Luis"    "Mary"  "Paty"
## [29,] "Adriana" "Alexei"  "Jazhiel" "Luis"    "Olga"  "Paty"
## [30,] "Adriana" "Alexei"  "Jazhiel" "Mary"    "Olga"  "Paty"
## [31,] "Adriana" "Alexei"  "Jesus"   "Luis"    "Mary"  "Olga"
## [32,] "Adriana" "Alexei"  "Jesus"   "Luis"    "Mary"  "Paty"
## [33,] "Adriana" "Alexei"  "Jesus"   "Luis"    "Olga"  "Paty"
## [34,] "Adriana" "Alexei"  "Jesus"   "Mary"    "Olga"  "Paty"
## [35,] "Adriana" "Alexei"  "Luis"    "Mary"    "Olga"  "Paty"
## [36,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Luis"  "Mary"
## [37,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Luis"  "Olga"
## [38,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Luis"  "Paty"
## [39,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Mary"  "Olga"
## [40,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Mary"  "Paty"
## [41,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Olga"  "Paty"
## [42,] "Adriana" "Caro"    "Jazhiel" "Luis"    "Mary"  "Olga"
## [43,] "Adriana" "Caro"    "Jazhiel" "Luis"    "Mary"  "Paty"
## [44,] "Adriana" "Caro"    "Jazhiel" "Luis"    "Olga"  "Paty"
## [45,] "Adriana" "Caro"    "Jazhiel" "Mary"    "Olga"  "Paty"
## [46,] "Adriana" "Caro"    "Jesus"   "Luis"    "Mary"  "Olga"
## [47,] "Adriana" "Caro"    "Jesus"   "Luis"    "Mary"  "Paty"
## [48,] "Adriana" "Caro"    "Jesus"   "Luis"    "Olga"  "Paty"
## [49,] "Adriana" "Caro"    "Jesus"   "Mary"    "Olga"  "Paty"
## [50,] "Adriana" "Caro"    "Luis"    "Mary"    "Olga"  "Paty"
## [51,] "Adriana" "Jazhiel" "Jesus"   "Luis"    "Mary"  "Olga"
## [52,] "Adriana" "Jazhiel" "Jesus"   "Luis"    "Mary"  "Paty"
## [53,] "Adriana" "Jazhiel" "Jesus"   "Luis"    "Olga"  "Paty"
## [54,] "Adriana" "Jazhiel" "Jesus"   "Mary"    "Olga"  "Paty"
## [55,] "Adriana" "Jazhiel" "Luis"    "Mary"    "Olga"  "Paty"
## [56,] "Adriana" "Jesus"   "Luis"    "Mary"    "Olga"  "Paty"

Pregunta 10: ¿En cuántas combinaciones de grupos seis está ‘Adriana’ en la primera o en la segunda o en la tercera columna?

combinaciones[which(combinaciones[,1] == 'Adriana' | combinaciones[,2] == 'Adriana' | combinaciones[,3] == 'Adriana'),]

##        [,1]      [,2]      [,3]      [,4]      [,5]      [,6]   
##   [1,] "Abraham" "Adriana" "Alexei"  "Caro"    "Jazhiel" "Jesus"
##   [2,] "Abraham" "Adriana" "Alexei"  "Caro"    "Jazhiel" "Luis" 
##   [3,] "Abraham" "Adriana" "Alexei"  "Caro"    "Jazhiel" "Mary" 
##   [4,] "Abraham" "Adriana" "Alexei"  "Caro"    "Jazhiel" "Olga" 
##   [5,] "Abraham" "Adriana" "Alexei"  "Caro"    "Jazhiel" "Paty" 
##   [6,] "Abraham" "Adriana" "Alexei"  "Caro"    "Jesus"   "Luis" 
##   [7,] "Abraham" "Adriana" "Alexei"  "Caro"    "Jesus"   "Mary" 
##   [8,] "Abraham" "Adriana" "Alexei"  "Caro"    "Jesus"   "Olga" 
##   [9,] "Abraham" "Adriana" "Alexei"  "Caro"    "Jesus"   "Paty" 
##  [10,] "Abraham" "Adriana" "Alexei"  "Caro"    "Luis"    "Mary" 
##  [11,] "Abraham" "Adriana" "Alexei"  "Caro"    "Luis"    "Olga" 
##  [12,] "Abraham" "Adriana" "Alexei"  "Caro"    "Luis"    "Paty" 
##  [13,] "Abraham" "Adriana" "Alexei"  "Caro"    "Mary"    "Olga" 
##  [14,] "Abraham" "Adriana" "Alexei"  "Caro"    "Mary"    "Paty" 
##  [15,] "Abraham" "Adriana" "Alexei"  "Caro"    "Olga"    "Paty" 
##  [16,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Luis" 
##  [17,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Mary" 
##  [18,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Olga" 
##  [19,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Paty" 
##  [20,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Luis"    "Mary" 
##  [21,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Luis"    "Olga" 
##  [22,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Luis"    "Paty" 
##  [23,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Mary"    "Olga" 
##  [24,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Mary"    "Paty" 
##  [25,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Olga"    "Paty" 
##  [26,] "Abraham" "Adriana" "Alexei"  "Jesus"   "Luis"    "Mary" 
##  [27,] "Abraham" "Adriana" "Alexei"  "Jesus"   "Luis"    "Olga" 
##  [28,] "Abraham" "Adriana" "Alexei"  "Jesus"   "Luis"    "Paty" 
##  [29,] "Abraham" "Adriana" "Alexei"  "Jesus"   "Mary"    "Olga" 
##  [30,] "Abraham" "Adriana" "Alexei"  "Jesus"   "Mary"    "Paty" 
##  [31,] "Abraham" "Adriana" "Alexei"  "Jesus"   "Olga"    "Paty" 
##  [32,] "Abraham" "Adriana" "Alexei"  "Luis"    "Mary"    "Olga" 
##  [33,] "Abraham" "Adriana" "Alexei"  "Luis"    "Mary"    "Paty" 
##  [34,] "Abraham" "Adriana" "Alexei"  "Luis"    "Olga"    "Paty" 
##  [35,] "Abraham" "Adriana" "Alexei"  "Mary"    "Olga"    "Paty" 
##  [36,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Jesus"   "Luis" 
##  [37,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Jesus"   "Mary" 
##  [38,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Jesus"   "Olga" 
##  [39,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Jesus"   "Paty" 
##  [40,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Luis"    "Mary" 
##  [41,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Luis"    "Olga" 
##  [42,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Luis"    "Paty" 
##  [43,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Mary"    "Olga" 
##  [44,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Mary"    "Paty" 
##  [45,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Olga"    "Paty" 
##  [46,] "Abraham" "Adriana" "Caro"    "Jesus"   "Luis"    "Mary" 
##  [47,] "Abraham" "Adriana" "Caro"    "Jesus"   "Luis"    "Olga" 
##  [48,] "Abraham" "Adriana" "Caro"    "Jesus"   "Luis"    "Paty" 
##  [49,] "Abraham" "Adriana" "Caro"    "Jesus"   "Mary"    "Olga" 
##  [50,] "Abraham" "Adriana" "Caro"    "Jesus"   "Mary"    "Paty" 
##  [51,] "Abraham" "Adriana" "Caro"    "Jesus"   "Olga"    "Paty" 
##  [52,] "Abraham" "Adriana" "Caro"    "Luis"    "Mary"    "Olga" 
##  [53,] "Abraham" "Adriana" "Caro"    "Luis"    "Mary"    "Paty" 
##  [54,] "Abraham" "Adriana" "Caro"    "Luis"    "Olga"    "Paty" 
##  [55,] "Abraham" "Adriana" "Caro"    "Mary"    "Olga"    "Paty" 
##  [56,] "Abraham" "Adriana" "Jazhiel" "Jesus"   "Luis"    "Mary" 
##  [57,] "Abraham" "Adriana" "Jazhiel" "Jesus"   "Luis"    "Olga" 
##  [58,] "Abraham" "Adriana" "Jazhiel" "Jesus"   "Luis"    "Paty" 
##  [59,] "Abraham" "Adriana" "Jazhiel" "Jesus"   "Mary"    "Olga" 
##  [60,] "Abraham" "Adriana" "Jazhiel" "Jesus"   "Mary"    "Paty" 
##  [61,] "Abraham" "Adriana" "Jazhiel" "Jesus"   "Olga"    "Paty" 
##  [62,] "Abraham" "Adriana" "Jazhiel" "Luis"    "Mary"    "Olga" 
##  [63,] "Abraham" "Adriana" "Jazhiel" "Luis"    "Mary"    "Paty" 
##  [64,] "Abraham" "Adriana" "Jazhiel" "Luis"    "Olga"    "Paty" 
##  [65,] "Abraham" "Adriana" "Jazhiel" "Mary"    "Olga"    "Paty" 
##  [66,] "Abraham" "Adriana" "Jesus"   "Luis"    "Mary"    "Olga" 
##  [67,] "Abraham" "Adriana" "Jesus"   "Luis"    "Mary"    "Paty" 
##  [68,] "Abraham" "Adriana" "Jesus"   "Luis"    "Olga"    "Paty" 
##  [69,] "Abraham" "Adriana" "Jesus"   "Mary"    "Olga"    "Paty" 
##  [70,] "Abraham" "Adriana" "Luis"    "Mary"    "Olga"    "Paty" 
##  [71,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Luis" 
##  [72,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Mary" 
##  [73,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Olga" 
##  [74,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Paty" 
##  [75,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Luis"    "Mary" 
##  [76,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Luis"    "Olga" 
##  [77,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Luis"    "Paty" 
##  [78,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Mary"    "Olga" 
##  [79,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Mary"    "Paty" 
##  [80,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Olga"    "Paty" 
##  [81,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Luis"    "Mary" 
##  [82,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Luis"    "Olga" 
##  [83,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Luis"    "Paty" 
##  [84,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Mary"    "Olga" 
##  [85,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Mary"    "Paty" 
##  [86,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Olga"    "Paty" 
##  [87,] "Adriana" "Alexei"  "Caro"    "Luis"    "Mary"    "Olga" 
##  [88,] "Adriana" "Alexei"  "Caro"    "Luis"    "Mary"    "Paty" 
##  [89,] "Adriana" "Alexei"  "Caro"    "Luis"    "Olga"    "Paty" 
##  [90,] "Adriana" "Alexei"  "Caro"    "Mary"    "Olga"    "Paty" 
##  [91,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Luis"    "Mary" 
##  [92,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Luis"    "Olga" 
##  [93,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Luis"    "Paty" 
##  [94,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Mary"    "Olga" 
##  [95,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Mary"    "Paty" 
##  [96,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Olga"    "Paty" 
##  [97,] "Adriana" "Alexei"  "Jazhiel" "Luis"    "Mary"    "Olga" 
##  [98,] "Adriana" "Alexei"  "Jazhiel" "Luis"    "Mary"    "Paty" 
##  [99,] "Adriana" "Alexei"  "Jazhiel" "Luis"    "Olga"    "Paty" 
## [100,] "Adriana" "Alexei"  "Jazhiel" "Mary"    "Olga"    "Paty" 
## [101,] "Adriana" "Alexei"  "Jesus"   "Luis"    "Mary"    "Olga" 
## [102,] "Adriana" "Alexei"  "Jesus"   "Luis"    "Mary"    "Paty" 
## [103,] "Adriana" "Alexei"  "Jesus"   "Luis"    "Olga"    "Paty" 
## [104,] "Adriana" "Alexei"  "Jesus"   "Mary"    "Olga"    "Paty" 
## [105,] "Adriana" "Alexei"  "Luis"    "Mary"    "Olga"    "Paty" 
## [106,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Luis"    "Mary" 
## [107,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Luis"    "Olga" 
## [108,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Luis"    "Paty" 
## [109,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Mary"    "Olga" 
## [110,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Mary"    "Paty" 
## [111,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Olga"    "Paty" 
## [112,] "Adriana" "Caro"    "Jazhiel" "Luis"    "Mary"    "Olga" 
## [113,] "Adriana" "Caro"    "Jazhiel" "Luis"    "Mary"    "Paty" 
## [114,] "Adriana" "Caro"    "Jazhiel" "Luis"    "Olga"    "Paty" 
## [115,] "Adriana" "Caro"    "Jazhiel" "Mary"    "Olga"    "Paty" 
## [116,] "Adriana" "Caro"    "Jesus"   "Luis"    "Mary"    "Olga" 
## [117,] "Adriana" "Caro"    "Jesus"   "Luis"    "Mary"    "Paty" 
## [118,] "Adriana" "Caro"    "Jesus"   "Luis"    "Olga"    "Paty" 
## [119,] "Adriana" "Caro"    "Jesus"   "Mary"    "Olga"    "Paty" 
## [120,] "Adriana" "Caro"    "Luis"    "Mary"    "Olga"    "Paty" 
## [121,] "Adriana" "Jazhiel" "Jesus"   "Luis"    "Mary"    "Olga" 
## [122,] "Adriana" "Jazhiel" "Jesus"   "Luis"    "Mary"    "Paty" 
## [123,] "Adriana" "Jazhiel" "Jesus"   "Luis"    "Olga"    "Paty" 
## [124,] "Adriana" "Jazhiel" "Jesus"   "Mary"    "Olga"    "Paty" 
## [125,] "Adriana" "Jazhiel" "Luis"    "Mary"    "Olga"    "Paty" 
## [126,] "Adriana" "Jesus"   "Luis"    "Mary"    "Olga"    "Paty"

Pregunta 11: ¿En cuántas combinaciones de grupos seis está ‘Paty’ en la cuarta o en la quinta o en la sexta columna?

combinaciones[which(combinaciones[,4] == 'Paty' | combinaciones[,5] == 'Paty' | combinaciones[,6] == 'Paty'),]

##        [,1]      [,2]      [,3]      [,4]      [,5]      [,6]  
##   [1,] "Abraham" "Adriana" "Alexei"  "Caro"    "Jazhiel" "Paty"
##   [2,] "Abraham" "Adriana" "Alexei"  "Caro"    "Jesus"   "Paty"
##   [3,] "Abraham" "Adriana" "Alexei"  "Caro"    "Luis"    "Paty"
##   [4,] "Abraham" "Adriana" "Alexei"  "Caro"    "Mary"    "Paty"
##   [5,] "Abraham" "Adriana" "Alexei"  "Caro"    "Olga"    "Paty"
##   [6,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Paty"
##   [7,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Luis"    "Paty"
##   [8,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Mary"    "Paty"
##   [9,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Olga"    "Paty"
##  [10,] "Abraham" "Adriana" "Alexei"  "Jesus"   "Luis"    "Paty"
##  [11,] "Abraham" "Adriana" "Alexei"  "Jesus"   "Mary"    "Paty"
##  [12,] "Abraham" "Adriana" "Alexei"  "Jesus"   "Olga"    "Paty"
##  [13,] "Abraham" "Adriana" "Alexei"  "Luis"    "Mary"    "Paty"
##  [14,] "Abraham" "Adriana" "Alexei"  "Luis"    "Olga"    "Paty"
##  [15,] "Abraham" "Adriana" "Alexei"  "Mary"    "Olga"    "Paty"
##  [16,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Jesus"   "Paty"
##  [17,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Luis"    "Paty"
##  [18,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Mary"    "Paty"
##  [19,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Olga"    "Paty"
##  [20,] "Abraham" "Adriana" "Caro"    "Jesus"   "Luis"    "Paty"
##  [21,] "Abraham" "Adriana" "Caro"    "Jesus"   "Mary"    "Paty"
##  [22,] "Abraham" "Adriana" "Caro"    "Jesus"   "Olga"    "Paty"
##  [23,] "Abraham" "Adriana" "Caro"    "Luis"    "Mary"    "Paty"
##  [24,] "Abraham" "Adriana" "Caro"    "Luis"    "Olga"    "Paty"
##  [25,] "Abraham" "Adriana" "Caro"    "Mary"    "Olga"    "Paty"
##  [26,] "Abraham" "Adriana" "Jazhiel" "Jesus"   "Luis"    "Paty"
##  [27,] "Abraham" "Adriana" "Jazhiel" "Jesus"   "Mary"    "Paty"
##  [28,] "Abraham" "Adriana" "Jazhiel" "Jesus"   "Olga"    "Paty"
##  [29,] "Abraham" "Adriana" "Jazhiel" "Luis"    "Mary"    "Paty"
##  [30,] "Abraham" "Adriana" "Jazhiel" "Luis"    "Olga"    "Paty"
##  [31,] "Abraham" "Adriana" "Jazhiel" "Mary"    "Olga"    "Paty"
##  [32,] "Abraham" "Adriana" "Jesus"   "Luis"    "Mary"    "Paty"
##  [33,] "Abraham" "Adriana" "Jesus"   "Luis"    "Olga"    "Paty"
##  [34,] "Abraham" "Adriana" "Jesus"   "Mary"    "Olga"    "Paty"
##  [35,] "Abraham" "Adriana" "Luis"    "Mary"    "Olga"    "Paty"
##  [36,] "Abraham" "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Paty"
##  [37,] "Abraham" "Alexei"  "Caro"    "Jazhiel" "Luis"    "Paty"
##  [38,] "Abraham" "Alexei"  "Caro"    "Jazhiel" "Mary"    "Paty"
##  [39,] "Abraham" "Alexei"  "Caro"    "Jazhiel" "Olga"    "Paty"
##  [40,] "Abraham" "Alexei"  "Caro"    "Jesus"   "Luis"    "Paty"
##  [41,] "Abraham" "Alexei"  "Caro"    "Jesus"   "Mary"    "Paty"
##  [42,] "Abraham" "Alexei"  "Caro"    "Jesus"   "Olga"    "Paty"
##  [43,] "Abraham" "Alexei"  "Caro"    "Luis"    "Mary"    "Paty"
##  [44,] "Abraham" "Alexei"  "Caro"    "Luis"    "Olga"    "Paty"
##  [45,] "Abraham" "Alexei"  "Caro"    "Mary"    "Olga"    "Paty"
##  [46,] "Abraham" "Alexei"  "Jazhiel" "Jesus"   "Luis"    "Paty"
##  [47,] "Abraham" "Alexei"  "Jazhiel" "Jesus"   "Mary"    "Paty"
##  [48,] "Abraham" "Alexei"  "Jazhiel" "Jesus"   "Olga"    "Paty"
##  [49,] "Abraham" "Alexei"  "Jazhiel" "Luis"    "Mary"    "Paty"
##  [50,] "Abraham" "Alexei"  "Jazhiel" "Luis"    "Olga"    "Paty"
##  [51,] "Abraham" "Alexei"  "Jazhiel" "Mary"    "Olga"    "Paty"
##  [52,] "Abraham" "Alexei"  "Jesus"   "Luis"    "Mary"    "Paty"
##  [53,] "Abraham" "Alexei"  "Jesus"   "Luis"    "Olga"    "Paty"
##  [54,] "Abraham" "Alexei"  "Jesus"   "Mary"    "Olga"    "Paty"
##  [55,] "Abraham" "Alexei"  "Luis"    "Mary"    "Olga"    "Paty"
##  [56,] "Abraham" "Caro"    "Jazhiel" "Jesus"   "Luis"    "Paty"
##  [57,] "Abraham" "Caro"    "Jazhiel" "Jesus"   "Mary"    "Paty"
##  [58,] "Abraham" "Caro"    "Jazhiel" "Jesus"   "Olga"    "Paty"
##  [59,] "Abraham" "Caro"    "Jazhiel" "Luis"    "Mary"    "Paty"
##  [60,] "Abraham" "Caro"    "Jazhiel" "Luis"    "Olga"    "Paty"
##  [61,] "Abraham" "Caro"    "Jazhiel" "Mary"    "Olga"    "Paty"
##  [62,] "Abraham" "Caro"    "Jesus"   "Luis"    "Mary"    "Paty"
##  [63,] "Abraham" "Caro"    "Jesus"   "Luis"    "Olga"    "Paty"
##  [64,] "Abraham" "Caro"    "Jesus"   "Mary"    "Olga"    "Paty"
##  [65,] "Abraham" "Caro"    "Luis"    "Mary"    "Olga"    "Paty"
##  [66,] "Abraham" "Jazhiel" "Jesus"   "Luis"    "Mary"    "Paty"
##  [67,] "Abraham" "Jazhiel" "Jesus"   "Luis"    "Olga"    "Paty"
##  [68,] "Abraham" "Jazhiel" "Jesus"   "Mary"    "Olga"    "Paty"
##  [69,] "Abraham" "Jazhiel" "Luis"    "Mary"    "Olga"    "Paty"
##  [70,] "Abraham" "Jesus"   "Luis"    "Mary"    "Olga"    "Paty"
##  [71,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Paty"
##  [72,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Luis"    "Paty"
##  [73,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Mary"    "Paty"
##  [74,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Olga"    "Paty"
##  [75,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Luis"    "Paty"
##  [76,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Mary"    "Paty"
##  [77,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Olga"    "Paty"
##  [78,] "Adriana" "Alexei"  "Caro"    "Luis"    "Mary"    "Paty"
##  [79,] "Adriana" "Alexei"  "Caro"    "Luis"    "Olga"    "Paty"
##  [80,] "Adriana" "Alexei"  "Caro"    "Mary"    "Olga"    "Paty"
##  [81,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Luis"    "Paty"
##  [82,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Mary"    "Paty"
##  [83,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Olga"    "Paty"
##  [84,] "Adriana" "Alexei"  "Jazhiel" "Luis"    "Mary"    "Paty"
##  [85,] "Adriana" "Alexei"  "Jazhiel" "Luis"    "Olga"    "Paty"
##  [86,] "Adriana" "Alexei"  "Jazhiel" "Mary"    "Olga"    "Paty"
##  [87,] "Adriana" "Alexei"  "Jesus"   "Luis"    "Mary"    "Paty"
##  [88,] "Adriana" "Alexei"  "Jesus"   "Luis"    "Olga"    "Paty"
##  [89,] "Adriana" "Alexei"  "Jesus"   "Mary"    "Olga"    "Paty"
##  [90,] "Adriana" "Alexei"  "Luis"    "Mary"    "Olga"    "Paty"
##  [91,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Luis"    "Paty"
##  [92,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Mary"    "Paty"
##  [93,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Olga"    "Paty"
##  [94,] "Adriana" "Caro"    "Jazhiel" "Luis"    "Mary"    "Paty"
##  [95,] "Adriana" "Caro"    "Jazhiel" "Luis"    "Olga"    "Paty"
##  [96,] "Adriana" "Caro"    "Jazhiel" "Mary"    "Olga"    "Paty"
##  [97,] "Adriana" "Caro"    "Jesus"   "Luis"    "Mary"    "Paty"
##  [98,] "Adriana" "Caro"    "Jesus"   "Luis"    "Olga"    "Paty"
##  [99,] "Adriana" "Caro"    "Jesus"   "Mary"    "Olga"    "Paty"
## [100,] "Adriana" "Caro"    "Luis"    "Mary"    "Olga"    "Paty"
## [101,] "Adriana" "Jazhiel" "Jesus"   "Luis"    "Mary"    "Paty"
## [102,] "Adriana" "Jazhiel" "Jesus"   "Luis"    "Olga"    "Paty"
## [103,] "Adriana" "Jazhiel" "Jesus"   "Mary"    "Olga"    "Paty"
## [104,] "Adriana" "Jazhiel" "Luis"    "Mary"    "Olga"    "Paty"
## [105,] "Adriana" "Jesus"   "Luis"    "Mary"    "Olga"    "Paty"
## [106,] "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Luis"    "Paty"
## [107,] "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Mary"    "Paty"
## [108,] "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Olga"    "Paty"
## [109,] "Alexei"  "Caro"    "Jazhiel" "Luis"    "Mary"    "Paty"
## [110,] "Alexei"  "Caro"    "Jazhiel" "Luis"    "Olga"    "Paty"
## [111,] "Alexei"  "Caro"    "Jazhiel" "Mary"    "Olga"    "Paty"
## [112,] "Alexei"  "Caro"    "Jesus"   "Luis"    "Mary"    "Paty"
## [113,] "Alexei"  "Caro"    "Jesus"   "Luis"    "Olga"    "Paty"
## [114,] "Alexei"  "Caro"    "Jesus"   "Mary"    "Olga"    "Paty"
## [115,] "Alexei"  "Caro"    "Luis"    "Mary"    "Olga"    "Paty"
## [116,] "Alexei"  "Jazhiel" "Jesus"   "Luis"    "Mary"    "Paty"
## [117,] "Alexei"  "Jazhiel" "Jesus"   "Luis"    "Olga"    "Paty"
## [118,] "Alexei"  "Jazhiel" "Jesus"   "Mary"    "Olga"    "Paty"
## [119,] "Alexei"  "Jazhiel" "Luis"    "Mary"    "Olga"    "Paty"
## [120,] "Alexei"  "Jesus"   "Luis"    "Mary"    "Olga"    "Paty"
## [121,] "Caro"    "Jazhiel" "Jesus"   "Luis"    "Mary"    "Paty"
## [122,] "Caro"    "Jazhiel" "Jesus"   "Luis"    "Olga"    "Paty"
## [123,] "Caro"    "Jazhiel" "Jesus"   "Mary"    "Olga"    "Paty"
## [124,] "Caro"    "Jazhiel" "Luis"    "Mary"    "Olga"    "Paty"
## [125,] "Caro"    "Jesus"   "Luis"    "Mary"    "Olga"    "Paty"
## [126,] "Jazhiel" "Jesus"   "Luis"    "Mary"    "Olga"    "Paty"

Pregunta 12: ¿En cuántas combinaciones de grupos seis está ‘Olga’ en la cuarta o en la quinta o en la sexta columna?

combinaciones[which(combinaciones[,4] == 'Olga' | combinaciones[,5] == 'Olga' | combinaciones[,6] == 'Olga'),]

##        [,1]      [,2]      [,3]      [,4]      [,5]      [,6]  
##   [1,] "Abraham" "Adriana" "Alexei"  "Caro"    "Jazhiel" "Olga"
##   [2,] "Abraham" "Adriana" "Alexei"  "Caro"    "Jesus"   "Olga"
##   [3,] "Abraham" "Adriana" "Alexei"  "Caro"    "Luis"    "Olga"
##   [4,] "Abraham" "Adriana" "Alexei"  "Caro"    "Mary"    "Olga"
##   [5,] "Abraham" "Adriana" "Alexei"  "Caro"    "Olga"    "Paty"
##   [6,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Olga"
##   [7,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Luis"    "Olga"
##   [8,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Mary"    "Olga"
##   [9,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Olga"    "Paty"
##  [10,] "Abraham" "Adriana" "Alexei"  "Jesus"   "Luis"    "Olga"
##  [11,] "Abraham" "Adriana" "Alexei"  "Jesus"   "Mary"    "Olga"
##  [12,] "Abraham" "Adriana" "Alexei"  "Jesus"   "Olga"    "Paty"
##  [13,] "Abraham" "Adriana" "Alexei"  "Luis"    "Mary"    "Olga"
##  [14,] "Abraham" "Adriana" "Alexei"  "Luis"    "Olga"    "Paty"
##  [15,] "Abraham" "Adriana" "Alexei"  "Mary"    "Olga"    "Paty"
##  [16,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Jesus"   "Olga"
##  [17,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Luis"    "Olga"
##  [18,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Mary"    "Olga"
##  [19,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Olga"    "Paty"
##  [20,] "Abraham" "Adriana" "Caro"    "Jesus"   "Luis"    "Olga"
##  [21,] "Abraham" "Adriana" "Caro"    "Jesus"   "Mary"    "Olga"
##  [22,] "Abraham" "Adriana" "Caro"    "Jesus"   "Olga"    "Paty"
##  [23,] "Abraham" "Adriana" "Caro"    "Luis"    "Mary"    "Olga"
##  [24,] "Abraham" "Adriana" "Caro"    "Luis"    "Olga"    "Paty"
##  [25,] "Abraham" "Adriana" "Caro"    "Mary"    "Olga"    "Paty"
##  [26,] "Abraham" "Adriana" "Jazhiel" "Jesus"   "Luis"    "Olga"
##  [27,] "Abraham" "Adriana" "Jazhiel" "Jesus"   "Mary"    "Olga"
##  [28,] "Abraham" "Adriana" "Jazhiel" "Jesus"   "Olga"    "Paty"
##  [29,] "Abraham" "Adriana" "Jazhiel" "Luis"    "Mary"    "Olga"
##  [30,] "Abraham" "Adriana" "Jazhiel" "Luis"    "Olga"    "Paty"
##  [31,] "Abraham" "Adriana" "Jazhiel" "Mary"    "Olga"    "Paty"
##  [32,] "Abraham" "Adriana" "Jesus"   "Luis"    "Mary"    "Olga"
##  [33,] "Abraham" "Adriana" "Jesus"   "Luis"    "Olga"    "Paty"
##  [34,] "Abraham" "Adriana" "Jesus"   "Mary"    "Olga"    "Paty"
##  [35,] "Abraham" "Adriana" "Luis"    "Mary"    "Olga"    "Paty"
##  [36,] "Abraham" "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Olga"
##  [37,] "Abraham" "Alexei"  "Caro"    "Jazhiel" "Luis"    "Olga"
##  [38,] "Abraham" "Alexei"  "Caro"    "Jazhiel" "Mary"    "Olga"
##  [39,] "Abraham" "Alexei"  "Caro"    "Jazhiel" "Olga"    "Paty"
##  [40,] "Abraham" "Alexei"  "Caro"    "Jesus"   "Luis"    "Olga"
##  [41,] "Abraham" "Alexei"  "Caro"    "Jesus"   "Mary"    "Olga"
##  [42,] "Abraham" "Alexei"  "Caro"    "Jesus"   "Olga"    "Paty"
##  [43,] "Abraham" "Alexei"  "Caro"    "Luis"    "Mary"    "Olga"
##  [44,] "Abraham" "Alexei"  "Caro"    "Luis"    "Olga"    "Paty"
##  [45,] "Abraham" "Alexei"  "Caro"    "Mary"    "Olga"    "Paty"
##  [46,] "Abraham" "Alexei"  "Jazhiel" "Jesus"   "Luis"    "Olga"
##  [47,] "Abraham" "Alexei"  "Jazhiel" "Jesus"   "Mary"    "Olga"
##  [48,] "Abraham" "Alexei"  "Jazhiel" "Jesus"   "Olga"    "Paty"
##  [49,] "Abraham" "Alexei"  "Jazhiel" "Luis"    "Mary"    "Olga"
##  [50,] "Abraham" "Alexei"  "Jazhiel" "Luis"    "Olga"    "Paty"
##  [51,] "Abraham" "Alexei"  "Jazhiel" "Mary"    "Olga"    "Paty"
##  [52,] "Abraham" "Alexei"  "Jesus"   "Luis"    "Mary"    "Olga"
##  [53,] "Abraham" "Alexei"  "Jesus"   "Luis"    "Olga"    "Paty"
##  [54,] "Abraham" "Alexei"  "Jesus"   "Mary"    "Olga"    "Paty"
##  [55,] "Abraham" "Alexei"  "Luis"    "Mary"    "Olga"    "Paty"
##  [56,] "Abraham" "Caro"    "Jazhiel" "Jesus"   "Luis"    "Olga"
##  [57,] "Abraham" "Caro"    "Jazhiel" "Jesus"   "Mary"    "Olga"
##  [58,] "Abraham" "Caro"    "Jazhiel" "Jesus"   "Olga"    "Paty"
##  [59,] "Abraham" "Caro"    "Jazhiel" "Luis"    "Mary"    "Olga"
##  [60,] "Abraham" "Caro"    "Jazhiel" "Luis"    "Olga"    "Paty"
##  [61,] "Abraham" "Caro"    "Jazhiel" "Mary"    "Olga"    "Paty"
##  [62,] "Abraham" "Caro"    "Jesus"   "Luis"    "Mary"    "Olga"
##  [63,] "Abraham" "Caro"    "Jesus"   "Luis"    "Olga"    "Paty"
##  [64,] "Abraham" "Caro"    "Jesus"   "Mary"    "Olga"    "Paty"
##  [65,] "Abraham" "Caro"    "Luis"    "Mary"    "Olga"    "Paty"
##  [66,] "Abraham" "Jazhiel" "Jesus"   "Luis"    "Mary"    "Olga"
##  [67,] "Abraham" "Jazhiel" "Jesus"   "Luis"    "Olga"    "Paty"
##  [68,] "Abraham" "Jazhiel" "Jesus"   "Mary"    "Olga"    "Paty"
##  [69,] "Abraham" "Jazhiel" "Luis"    "Mary"    "Olga"    "Paty"
##  [70,] "Abraham" "Jesus"   "Luis"    "Mary"    "Olga"    "Paty"
##  [71,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Olga"
##  [72,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Luis"    "Olga"
##  [73,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Mary"    "Olga"
##  [74,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Olga"    "Paty"
##  [75,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Luis"    "Olga"
##  [76,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Mary"    "Olga"
##  [77,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Olga"    "Paty"
##  [78,] "Adriana" "Alexei"  "Caro"    "Luis"    "Mary"    "Olga"
##  [79,] "Adriana" "Alexei"  "Caro"    "Luis"    "Olga"    "Paty"
##  [80,] "Adriana" "Alexei"  "Caro"    "Mary"    "Olga"    "Paty"
##  [81,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Luis"    "Olga"
##  [82,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Mary"    "Olga"
##  [83,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Olga"    "Paty"
##  [84,] "Adriana" "Alexei"  "Jazhiel" "Luis"    "Mary"    "Olga"
##  [85,] "Adriana" "Alexei"  "Jazhiel" "Luis"    "Olga"    "Paty"
##  [86,] "Adriana" "Alexei"  "Jazhiel" "Mary"    "Olga"    "Paty"
##  [87,] "Adriana" "Alexei"  "Jesus"   "Luis"    "Mary"    "Olga"
##  [88,] "Adriana" "Alexei"  "Jesus"   "Luis"    "Olga"    "Paty"
##  [89,] "Adriana" "Alexei"  "Jesus"   "Mary"    "Olga"    "Paty"
##  [90,] "Adriana" "Alexei"  "Luis"    "Mary"    "Olga"    "Paty"
##  [91,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Luis"    "Olga"
##  [92,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Mary"    "Olga"
##  [93,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Olga"    "Paty"
##  [94,] "Adriana" "Caro"    "Jazhiel" "Luis"    "Mary"    "Olga"
##  [95,] "Adriana" "Caro"    "Jazhiel" "Luis"    "Olga"    "Paty"
##  [96,] "Adriana" "Caro"    "Jazhiel" "Mary"    "Olga"    "Paty"
##  [97,] "Adriana" "Caro"    "Jesus"   "Luis"    "Mary"    "Olga"
##  [98,] "Adriana" "Caro"    "Jesus"   "Luis"    "Olga"    "Paty"
##  [99,] "Adriana" "Caro"    "Jesus"   "Mary"    "Olga"    "Paty"
## [100,] "Adriana" "Caro"    "Luis"    "Mary"    "Olga"    "Paty"
## [101,] "Adriana" "Jazhiel" "Jesus"   "Luis"    "Mary"    "Olga"
## [102,] "Adriana" "Jazhiel" "Jesus"   "Luis"    "Olga"    "Paty"
## [103,] "Adriana" "Jazhiel" "Jesus"   "Mary"    "Olga"    "Paty"
## [104,] "Adriana" "Jazhiel" "Luis"    "Mary"    "Olga"    "Paty"
## [105,] "Adriana" "Jesus"   "Luis"    "Mary"    "Olga"    "Paty"
## [106,] "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Luis"    "Olga"
## [107,] "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Mary"    "Olga"
## [108,] "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Olga"    "Paty"
## [109,] "Alexei"  "Caro"    "Jazhiel" "Luis"    "Mary"    "Olga"
## [110,] "Alexei"  "Caro"    "Jazhiel" "Luis"    "Olga"    "Paty"
## [111,] "Alexei"  "Caro"    "Jazhiel" "Mary"    "Olga"    "Paty"
## [112,] "Alexei"  "Caro"    "Jesus"   "Luis"    "Mary"    "Olga"
## [113,] "Alexei"  "Caro"    "Jesus"   "Luis"    "Olga"    "Paty"
## [114,] "Alexei"  "Caro"    "Jesus"   "Mary"    "Olga"    "Paty"
## [115,] "Alexei"  "Caro"    "Luis"    "Mary"    "Olga"    "Paty"
## [116,] "Alexei"  "Jazhiel" "Jesus"   "Luis"    "Mary"    "Olga"
## [117,] "Alexei"  "Jazhiel" "Jesus"   "Luis"    "Olga"    "Paty"
## [118,] "Alexei"  "Jazhiel" "Jesus"   "Mary"    "Olga"    "Paty"
## [119,] "Alexei"  "Jazhiel" "Luis"    "Mary"    "Olga"    "Paty"
## [120,] "Alexei"  "Jesus"   "Luis"    "Mary"    "Olga"    "Paty"
## [121,] "Caro"    "Jazhiel" "Jesus"   "Luis"    "Mary"    "Olga"
## [122,] "Caro"    "Jazhiel" "Jesus"   "Luis"    "Olga"    "Paty"
## [123,] "Caro"    "Jazhiel" "Jesus"   "Mary"    "Olga"    "Paty"
## [124,] "Caro"    "Jazhiel" "Luis"    "Mary"    "Olga"    "Paty"
## [125,] "Caro"    "Jesus"   "Luis"    "Mary"    "Olga"    "Paty"
## [126,] "Jazhiel" "Jesus"   "Luis"    "Mary"    "Olga"    "Paty"

Pregunta 13: ¿En cuántas combinaciones de grupos seis está ‘Olga’ en cualquier columna de la 1 a la 6?

combinaciones[which(combinaciones[,1] == 'Olga' | combinaciones[,2] == 'Olga' | combinaciones[,3] == 'Olga' | combinaciones[,4] == 'Olga' | combinaciones[,5] == 'Olga' | combinaciones[,6] == 'Olga'),]

##        [,1]      [,2]      [,3]      [,4]      [,5]      [,6]  
##   [1,] "Abraham" "Adriana" "Alexei"  "Caro"    "Jazhiel" "Olga"
##   [2,] "Abraham" "Adriana" "Alexei"  "Caro"    "Jesus"   "Olga"
##   [3,] "Abraham" "Adriana" "Alexei"  "Caro"    "Luis"    "Olga"
##   [4,] "Abraham" "Adriana" "Alexei"  "Caro"    "Mary"    "Olga"
##   [5,] "Abraham" "Adriana" "Alexei"  "Caro"    "Olga"    "Paty"
##   [6,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Olga"
##   [7,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Luis"    "Olga"
##   [8,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Mary"    "Olga"
##   [9,] "Abraham" "Adriana" "Alexei"  "Jazhiel" "Olga"    "Paty"
##  [10,] "Abraham" "Adriana" "Alexei"  "Jesus"   "Luis"    "Olga"
##  [11,] "Abraham" "Adriana" "Alexei"  "Jesus"   "Mary"    "Olga"
##  [12,] "Abraham" "Adriana" "Alexei"  "Jesus"   "Olga"    "Paty"
##  [13,] "Abraham" "Adriana" "Alexei"  "Luis"    "Mary"    "Olga"
##  [14,] "Abraham" "Adriana" "Alexei"  "Luis"    "Olga"    "Paty"
##  [15,] "Abraham" "Adriana" "Alexei"  "Mary"    "Olga"    "Paty"
##  [16,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Jesus"   "Olga"
##  [17,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Luis"    "Olga"
##  [18,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Mary"    "Olga"
##  [19,] "Abraham" "Adriana" "Caro"    "Jazhiel" "Olga"    "Paty"
##  [20,] "Abraham" "Adriana" "Caro"    "Jesus"   "Luis"    "Olga"
##  [21,] "Abraham" "Adriana" "Caro"    "Jesus"   "Mary"    "Olga"
##  [22,] "Abraham" "Adriana" "Caro"    "Jesus"   "Olga"    "Paty"
##  [23,] "Abraham" "Adriana" "Caro"    "Luis"    "Mary"    "Olga"
##  [24,] "Abraham" "Adriana" "Caro"    "Luis"    "Olga"    "Paty"
##  [25,] "Abraham" "Adriana" "Caro"    "Mary"    "Olga"    "Paty"
##  [26,] "Abraham" "Adriana" "Jazhiel" "Jesus"   "Luis"    "Olga"
##  [27,] "Abraham" "Adriana" "Jazhiel" "Jesus"   "Mary"    "Olga"
##  [28,] "Abraham" "Adriana" "Jazhiel" "Jesus"   "Olga"    "Paty"
##  [29,] "Abraham" "Adriana" "Jazhiel" "Luis"    "Mary"    "Olga"
##  [30,] "Abraham" "Adriana" "Jazhiel" "Luis"    "Olga"    "Paty"
##  [31,] "Abraham" "Adriana" "Jazhiel" "Mary"    "Olga"    "Paty"
##  [32,] "Abraham" "Adriana" "Jesus"   "Luis"    "Mary"    "Olga"
##  [33,] "Abraham" "Adriana" "Jesus"   "Luis"    "Olga"    "Paty"
##  [34,] "Abraham" "Adriana" "Jesus"   "Mary"    "Olga"    "Paty"
##  [35,] "Abraham" "Adriana" "Luis"    "Mary"    "Olga"    "Paty"
##  [36,] "Abraham" "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Olga"
##  [37,] "Abraham" "Alexei"  "Caro"    "Jazhiel" "Luis"    "Olga"
##  [38,] "Abraham" "Alexei"  "Caro"    "Jazhiel" "Mary"    "Olga"
##  [39,] "Abraham" "Alexei"  "Caro"    "Jazhiel" "Olga"    "Paty"
##  [40,] "Abraham" "Alexei"  "Caro"    "Jesus"   "Luis"    "Olga"
##  [41,] "Abraham" "Alexei"  "Caro"    "Jesus"   "Mary"    "Olga"
##  [42,] "Abraham" "Alexei"  "Caro"    "Jesus"   "Olga"    "Paty"
##  [43,] "Abraham" "Alexei"  "Caro"    "Luis"    "Mary"    "Olga"
##  [44,] "Abraham" "Alexei"  "Caro"    "Luis"    "Olga"    "Paty"
##  [45,] "Abraham" "Alexei"  "Caro"    "Mary"    "Olga"    "Paty"
##  [46,] "Abraham" "Alexei"  "Jazhiel" "Jesus"   "Luis"    "Olga"
##  [47,] "Abraham" "Alexei"  "Jazhiel" "Jesus"   "Mary"    "Olga"
##  [48,] "Abraham" "Alexei"  "Jazhiel" "Jesus"   "Olga"    "Paty"
##  [49,] "Abraham" "Alexei"  "Jazhiel" "Luis"    "Mary"    "Olga"
##  [50,] "Abraham" "Alexei"  "Jazhiel" "Luis"    "Olga"    "Paty"
##  [51,] "Abraham" "Alexei"  "Jazhiel" "Mary"    "Olga"    "Paty"
##  [52,] "Abraham" "Alexei"  "Jesus"   "Luis"    "Mary"    "Olga"
##  [53,] "Abraham" "Alexei"  "Jesus"   "Luis"    "Olga"    "Paty"
##  [54,] "Abraham" "Alexei"  "Jesus"   "Mary"    "Olga"    "Paty"
##  [55,] "Abraham" "Alexei"  "Luis"    "Mary"    "Olga"    "Paty"
##  [56,] "Abraham" "Caro"    "Jazhiel" "Jesus"   "Luis"    "Olga"
##  [57,] "Abraham" "Caro"    "Jazhiel" "Jesus"   "Mary"    "Olga"
##  [58,] "Abraham" "Caro"    "Jazhiel" "Jesus"   "Olga"    "Paty"
##  [59,] "Abraham" "Caro"    "Jazhiel" "Luis"    "Mary"    "Olga"
##  [60,] "Abraham" "Caro"    "Jazhiel" "Luis"    "Olga"    "Paty"
##  [61,] "Abraham" "Caro"    "Jazhiel" "Mary"    "Olga"    "Paty"
##  [62,] "Abraham" "Caro"    "Jesus"   "Luis"    "Mary"    "Olga"
##  [63,] "Abraham" "Caro"    "Jesus"   "Luis"    "Olga"    "Paty"
##  [64,] "Abraham" "Caro"    "Jesus"   "Mary"    "Olga"    "Paty"
##  [65,] "Abraham" "Caro"    "Luis"    "Mary"    "Olga"    "Paty"
##  [66,] "Abraham" "Jazhiel" "Jesus"   "Luis"    "Mary"    "Olga"
##  [67,] "Abraham" "Jazhiel" "Jesus"   "Luis"    "Olga"    "Paty"
##  [68,] "Abraham" "Jazhiel" "Jesus"   "Mary"    "Olga"    "Paty"
##  [69,] "Abraham" "Jazhiel" "Luis"    "Mary"    "Olga"    "Paty"
##  [70,] "Abraham" "Jesus"   "Luis"    "Mary"    "Olga"    "Paty"
##  [71,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Olga"
##  [72,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Luis"    "Olga"
##  [73,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Mary"    "Olga"
##  [74,] "Adriana" "Alexei"  "Caro"    "Jazhiel" "Olga"    "Paty"
##  [75,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Luis"    "Olga"
##  [76,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Mary"    "Olga"
##  [77,] "Adriana" "Alexei"  "Caro"    "Jesus"   "Olga"    "Paty"
##  [78,] "Adriana" "Alexei"  "Caro"    "Luis"    "Mary"    "Olga"
##  [79,] "Adriana" "Alexei"  "Caro"    "Luis"    "Olga"    "Paty"
##  [80,] "Adriana" "Alexei"  "Caro"    "Mary"    "Olga"    "Paty"
##  [81,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Luis"    "Olga"
##  [82,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Mary"    "Olga"
##  [83,] "Adriana" "Alexei"  "Jazhiel" "Jesus"   "Olga"    "Paty"
##  [84,] "Adriana" "Alexei"  "Jazhiel" "Luis"    "Mary"    "Olga"
##  [85,] "Adriana" "Alexei"  "Jazhiel" "Luis"    "Olga"    "Paty"
##  [86,] "Adriana" "Alexei"  "Jazhiel" "Mary"    "Olga"    "Paty"
##  [87,] "Adriana" "Alexei"  "Jesus"   "Luis"    "Mary"    "Olga"
##  [88,] "Adriana" "Alexei"  "Jesus"   "Luis"    "Olga"    "Paty"
##  [89,] "Adriana" "Alexei"  "Jesus"   "Mary"    "Olga"    "Paty"
##  [90,] "Adriana" "Alexei"  "Luis"    "Mary"    "Olga"    "Paty"
##  [91,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Luis"    "Olga"
##  [92,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Mary"    "Olga"
##  [93,] "Adriana" "Caro"    "Jazhiel" "Jesus"   "Olga"    "Paty"
##  [94,] "Adriana" "Caro"    "Jazhiel" "Luis"    "Mary"    "Olga"
##  [95,] "Adriana" "Caro"    "Jazhiel" "Luis"    "Olga"    "Paty"
##  [96,] "Adriana" "Caro"    "Jazhiel" "Mary"    "Olga"    "Paty"
##  [97,] "Adriana" "Caro"    "Jesus"   "Luis"    "Mary"    "Olga"
##  [98,] "Adriana" "Caro"    "Jesus"   "Luis"    "Olga"    "Paty"
##  [99,] "Adriana" "Caro"    "Jesus"   "Mary"    "Olga"    "Paty"
## [100,] "Adriana" "Caro"    "Luis"    "Mary"    "Olga"    "Paty"
## [101,] "Adriana" "Jazhiel" "Jesus"   "Luis"    "Mary"    "Olga"
## [102,] "Adriana" "Jazhiel" "Jesus"   "Luis"    "Olga"    "Paty"
## [103,] "Adriana" "Jazhiel" "Jesus"   "Mary"    "Olga"    "Paty"
## [104,] "Adriana" "Jazhiel" "Luis"    "Mary"    "Olga"    "Paty"
## [105,] "Adriana" "Jesus"   "Luis"    "Mary"    "Olga"    "Paty"
## [106,] "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Luis"    "Olga"
## [107,] "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Mary"    "Olga"
## [108,] "Alexei"  "Caro"    "Jazhiel" "Jesus"   "Olga"    "Paty"
## [109,] "Alexei"  "Caro"    "Jazhiel" "Luis"    "Mary"    "Olga"
## [110,] "Alexei"  "Caro"    "Jazhiel" "Luis"    "Olga"    "Paty"
## [111,] "Alexei"  "Caro"    "Jazhiel" "Mary"    "Olga"    "Paty"
## [112,] "Alexei"  "Caro"    "Jesus"   "Luis"    "Mary"    "Olga"
## [113,] "Alexei"  "Caro"    "Jesus"   "Luis"    "Olga"    "Paty"
## [114,] "Alexei"  "Caro"    "Jesus"   "Mary"    "Olga"    "Paty"
## [115,] "Alexei"  "Caro"    "Luis"    "Mary"    "Olga"    "Paty"
## [116,] "Alexei"  "Jazhiel" "Jesus"   "Luis"    "Mary"    "Olga"
## [117,] "Alexei"  "Jazhiel" "Jesus"   "Luis"    "Olga"    "Paty"
## [118,] "Alexei"  "Jazhiel" "Jesus"   "Mary"    "Olga"    "Paty"
## [119,] "Alexei"  "Jazhiel" "Luis"    "Mary"    "Olga"    "Paty"
## [120,] "Alexei"  "Jesus"   "Luis"    "Mary"    "Olga"    "Paty"
## [121,] "Caro"    "Jazhiel" "Jesus"   "Luis"    "Mary"    "Olga"
## [122,] "Caro"    "Jazhiel" "Jesus"   "Luis"    "Olga"    "Paty"
## [123,] "Caro"    "Jazhiel" "Jesus"   "Mary"    "Olga"    "Paty"
## [124,] "Caro"    "Jazhiel" "Luis"    "Mary"    "Olga"    "Paty"
## [125,] "Caro"    "Jesus"   "Luis"    "Mary"    "Olga"    "Paty"
## [126,] "Jazhiel" "Jesus"   "Luis"    "Mary"    "Olga"    "Paty"

Pregunta 14: ¿En cuántas combinaciones de grupos seis están ‘Adriana’, ‘Mary’, ‘Olga’ y ‘Paty’ en cualquier columna de la 1 a la 6. Deben de estar ellas, en cuáles y cuántas aparecen?

combinaciones[which((combinaciones[,1] == 'Adriana' | combinaciones[,2] == 'Adriana' | combinaciones[,3] == 'Adriana' | combinaciones[,4] == 'Adriana' | combinaciones[,5] == 'Adriana' | combinaciones[,6] == 'Adriana') & (combinaciones[,1] == 'Mary' | combinaciones[,2] == 'Mary' | combinaciones[,3] == 'Mary' | combinaciones[,4] == 'Mary' | combinaciones[,5] == 'Mary' | combinaciones[,6] == 'Mary') & (combinaciones[,1] == 'Olga' | combinaciones[,2] == 'Olga' | combinaciones[,3] == 'Olga' | combinaciones[,4] == 'Olga' | combinaciones[,5] == 'Olga' | combinaciones[,6] == 'Olga') & (combinaciones[,1] == 'Paty' | combinaciones[,2] == 'Paty' | combinaciones[,3] == 'Paty' | combinaciones[,4] == 'Paty' | combinaciones[,5] == 'Paty' | combinaciones[,6] == 'Paty')),]

##       [,1]      [,2]      [,3]      [,4]   [,5]   [,6]  
##  [1,] "Abraham" "Adriana" "Alexei"  "Mary" "Olga" "Paty"
##  [2,] "Abraham" "Adriana" "Caro"    "Mary" "Olga" "Paty"
##  [3,] "Abraham" "Adriana" "Jazhiel" "Mary" "Olga" "Paty"
##  [4,] "Abraham" "Adriana" "Jesus"   "Mary" "Olga" "Paty"
##  [5,] "Abraham" "Adriana" "Luis"    "Mary" "Olga" "Paty"
##  [6,] "Adriana" "Alexei"  "Caro"    "Mary" "Olga" "Paty"
##  [7,] "Adriana" "Alexei"  "Jazhiel" "Mary" "Olga" "Paty"
##  [8,] "Adriana" "Alexei"  "Jesus"   "Mary" "Olga" "Paty"
##  [9,] "Adriana" "Alexei"  "Luis"    "Mary" "Olga" "Paty"
## [10,] "Adriana" "Caro"    "Jazhiel" "Mary" "Olga" "Paty"
## [11,] "Adriana" "Caro"    "Jesus"   "Mary" "Olga" "Paty"
## [12,] "Adriana" "Caro"    "Luis"    "Mary" "Olga" "Paty"
## [13,] "Adriana" "Jazhiel" "Jesus"   "Mary" "Olga" "Paty"
## [14,] "Adriana" "Jazhiel" "Luis"    "Mary" "Olga" "Paty"
## [15,] "Adriana" "Jesus"   "Luis"    "Mary" "Olga" "Paty"

Pregunta 15: ¿En cuántas permutaciones de grupos seis está ‘Adriana’ en la primera o en la segunda o en la tercera columna?

head(permutaciones[which(permutaciones[,1] == 'Adriana' | permutaciones[,2] == 'Adriana' | permutaciones[,3] == 'Adriana'),])

##      [,1]      [,2]      [,3]     [,4]   [,5]      [,6]     
## [1,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Jesus"  
## [2,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Luis"   
## [3,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Mary"   
## [4,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Olga"   
## [5,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Paty"   
## [6,] "Abraham" "Adriana" "Alexei" "Caro" "Jesus"   "Jazhiel"

tail(permutaciones[which(permutaciones[,1] == 'Adriana' | permutaciones[,2] == 'Adriana' | permutaciones[,3] == 'Adriana'),])

##          [,1]   [,2]   [,3]      [,4]   [,5]    [,6]     
## [45355,] "Paty" "Olga" "Adriana" "Mary" "Jesus" "Luis"   
## [45356,] "Paty" "Olga" "Adriana" "Mary" "Luis"  "Abraham"
## [45357,] "Paty" "Olga" "Adriana" "Mary" "Luis"  "Alexei" 
## [45358,] "Paty" "Olga" "Adriana" "Mary" "Luis"  "Caro"   
## [45359,] "Paty" "Olga" "Adriana" "Mary" "Luis"  "Jazhiel"
## [45360,] "Paty" "Olga" "Adriana" "Mary" "Luis"  "Jesus"

Pregunta 16: ¿En cuántas permutaciones de grupos seis está ‘Paty’ en la cuarta o en la quinta o en la sexta columna?.

head(permutaciones[which(permutaciones[,4] == 'Paty' | permutaciones[,5] == 'Paty' | permutaciones[,6] == 'Paty'),])

##      [,1]      [,2]      [,3]     [,4]   [,5]      [,6]     
## [1,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Paty"   
## [2,] "Abraham" "Adriana" "Alexei" "Caro" "Jesus"   "Paty"   
## [3,] "Abraham" "Adriana" "Alexei" "Caro" "Luis"    "Paty"   
## [4,] "Abraham" "Adriana" "Alexei" "Caro" "Mary"    "Paty"   
## [5,] "Abraham" "Adriana" "Alexei" "Caro" "Olga"    "Paty"   
## [6,] "Abraham" "Adriana" "Alexei" "Caro" "Paty"    "Jazhiel"

tail(permutaciones[which(permutaciones[,4] == 'Paty' | permutaciones[,5] == 'Paty' | permutaciones[,6] == 'Paty'),])

##          [,1]   [,2]   [,3]   [,4]   [,5]      [,6]     
## [45355,] "Olga" "Mary" "Luis" "Paty" "Jazhiel" "Jesus"  
## [45356,] "Olga" "Mary" "Luis" "Paty" "Jesus"   "Abraham"
## [45357,] "Olga" "Mary" "Luis" "Paty" "Jesus"   "Adriana"
## [45358,] "Olga" "Mary" "Luis" "Paty" "Jesus"   "Alexei" 
## [45359,] "Olga" "Mary" "Luis" "Paty" "Jesus"   "Caro"   
## [45360,] "Olga" "Mary" "Luis" "Paty" "Jesus"   "Jazhiel"

Pregunta 17: ¿En cuántas permutaciones de grupos seis está ‘Olga’ en la cuarta o en la quinta o en la sexta columna?.

head(permutaciones[which(permutaciones[,4] == 'Olga' | permutaciones[,5] == 'Olga' | permutaciones[,6] == 'Olga'),])

##      [,1]      [,2]      [,3]     [,4]   [,5]      [,6]     
## [1,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Olga"   
## [2,] "Abraham" "Adriana" "Alexei" "Caro" "Jesus"   "Olga"   
## [3,] "Abraham" "Adriana" "Alexei" "Caro" "Luis"    "Olga"   
## [4,] "Abraham" "Adriana" "Alexei" "Caro" "Mary"    "Olga"   
## [5,] "Abraham" "Adriana" "Alexei" "Caro" "Olga"    "Jazhiel"
## [6,] "Abraham" "Adriana" "Alexei" "Caro" "Olga"    "Jesus"

tail(permutaciones[which(permutaciones[,4] == 'Olga' | permutaciones[,5] == 'Olga' | permutaciones[,6] == 'Olga'),])

##          [,1]   [,2]   [,3]   [,4]   [,5]      [,6]     
## [45355,] "Paty" "Mary" "Luis" "Olga" "Jazhiel" "Jesus"  
## [45356,] "Paty" "Mary" "Luis" "Olga" "Jesus"   "Abraham"
## [45357,] "Paty" "Mary" "Luis" "Olga" "Jesus"   "Adriana"
## [45358,] "Paty" "Mary" "Luis" "Olga" "Jesus"   "Alexei" 
## [45359,] "Paty" "Mary" "Luis" "Olga" "Jesus"   "Caro"   
## [45360,] "Paty" "Mary" "Luis" "Olga" "Jesus"   "Jazhiel"

Pregunta 18: ¿En cuántas permutaciones de grupos seis está ‘Olga’ en cualquier columna de la 1 a la 6?

head(permutaciones[which(permutaciones[,1] == 'Olga' | permutaciones[,2] == 'Olga' | permutaciones[,3] == 'Olga' | permutaciones[,4] == 'Olga' | permutaciones[,5] == 'Olga' | permutaciones[,6] == 'Olga'),])

##      [,1]      [,2]      [,3]     [,4]   [,5]      [,6]     
## [1,] "Abraham" "Adriana" "Alexei" "Caro" "Jazhiel" "Olga"   
## [2,] "Abraham" "Adriana" "Alexei" "Caro" "Jesus"   "Olga"   
## [3,] "Abraham" "Adriana" "Alexei" "Caro" "Luis"    "Olga"   
## [4,] "Abraham" "Adriana" "Alexei" "Caro" "Mary"    "Olga"   
## [5,] "Abraham" "Adriana" "Alexei" "Caro" "Olga"    "Jazhiel"
## [6,] "Abraham" "Adriana" "Alexei" "Caro" "Olga"    "Jesus"

tail(permutaciones[which(permutaciones[,1] == 'Olga' | permutaciones[,2] == 'Olga' | permutaciones[,3] == 'Olga' | permutaciones[,4] == 'Olga' | permutaciones[,5] == 'Olga' | permutaciones[,6] == 'Olga'),])

##          [,1]   [,2]   [,3]   [,4]   [,5]      [,6]     
## [90715,] "Paty" "Olga" "Mary" "Luis" "Jazhiel" "Jesus"  
## [90716,] "Paty" "Olga" "Mary" "Luis" "Jesus"   "Abraham"
## [90717,] "Paty" "Olga" "Mary" "Luis" "Jesus"   "Adriana"
## [90718,] "Paty" "Olga" "Mary" "Luis" "Jesus"   "Alexei" 
## [90719,] "Paty" "Olga" "Mary" "Luis" "Jesus"   "Caro"   
## [90720,] "Paty" "Olga" "Mary" "Luis" "Jesus"   "Jazhiel"

Pregunta 19: ¿En cuántas permutaciones de grupos seis están ‘Adriana’, ‘Mary’, ‘Olga’ y ‘Paty’ en cualquier columna de la 1 a la 6. Deben de estar ellas, en cuáles y cuántas aparecen?.

head(permutaciones[which((permutaciones[,1] == 'Adriana' | permutaciones[,2] == 'Adriana' | permutaciones[,3] == 'Adriana' | permutaciones[,4] == 'Adriana' | permutaciones[,5] == 'Adriana' | permutaciones[,6] == 'Adriana') & (permutaciones[,1] == 'Mary' | permutaciones[,2] == 'Mary' | combinaciones[,3] == 'Mary' | permutaciones[,4] == 'Mary' | permutaciones[,5] == 'Mary' | permutaciones[,6] == 'Mary') & (permutaciones[,1] == 'Olga' | permutaciones[,2] == 'Olga' | permutaciones[,3] == 'Olga' | permutaciones[,4] == 'Olga' | permutaciones[,5] == 'Olga' | permutaciones[,6] == 'Olga') & (permutaciones[,1] == 'Paty' | permutaciones[,2] == 'Paty' | permutaciones[,3] == 'Paty' | permutaciones[,4] == 'Paty' | permutaciones[,5] == 'Paty' | permutaciones[,6] == 'Paty')),])

##      [,1]      [,2]      [,3]     [,4]   [,5]   [,6]  
## [1,] "Abraham" "Adriana" "Alexei" "Mary" "Olga" "Paty"
## [2,] "Abraham" "Adriana" "Alexei" "Mary" "Paty" "Olga"
## [3,] "Abraham" "Adriana" "Alexei" "Olga" "Mary" "Paty"
## [4,] "Abraham" "Adriana" "Alexei" "Olga" "Paty" "Mary"
## [5,] "Abraham" "Adriana" "Alexei" "Paty" "Mary" "Olga"
## [6,] "Abraham" "Adriana" "Alexei" "Paty" "Olga" "Mary"

tail(permutaciones[which((permutaciones[,1] == 'Adriana' | permutaciones[,2] == 'Adriana' | permutaciones[,3] == 'Adriana' | permutaciones[,4] == 'Adriana' | permutaciones[,5] == 'Adriana' | permutaciones[,6] == 'Adriana') & (permutaciones[,1] == 'Mary' | permutaciones[,2] == 'Mary' | combinaciones[,3] == 'Mary' | permutaciones[,4] == 'Mary' | permutaciones[,5] == 'Mary' | permutaciones[,6] == 'Mary') & (permutaciones[,1] == 'Olga' | permutaciones[,2] == 'Olga' | permutaciones[,3] == 'Olga' | permutaciones[,4] == 'Olga' | permutaciones[,5] == 'Olga' | permutaciones[,6] == 'Olga') & (permutaciones[,1] == 'Paty' | permutaciones[,2] == 'Paty' | permutaciones[,3] == 'Paty' | permutaciones[,4] == 'Paty' | permutaciones[,5] == 'Paty' | permutaciones[,6] == 'Paty')),])

##         [,1]   [,2]   [,3]   [,4]   [,5]      [,6]     
## [8995,] "Paty" "Olga" "Luis" "Mary" "Adriana" "Jazhiel"
## [8996,] "Paty" "Olga" "Luis" "Mary" "Adriana" "Jesus"  
## [8997,] "Paty" "Olga" "Luis" "Mary" "Alexei"  "Adriana"
## [8998,] "Paty" "Olga" "Luis" "Mary" "Caro"    "Adriana"
## [8999,] "Paty" "Olga" "Luis" "Mary" "Jazhiel" "Adriana"
## [9000,] "Paty" "Olga" "Luis" "Mary" "Jesus"   "Adriana"

Pregunta 20: ¿En cuantas ocasiones de las PERMUTACIONES en grupos de SEIS se encuentra juntas “Adriana”, “Mary”, “Olga” y “Paty”. Ya sean en las columnas 1-4, o en las columnas 2-5, o en las columnas 3-6. en ese orden?.

permutaciones[which((permutaciones[,1] == 'Adriana' & permutaciones[,2] == 'Mary' & permutaciones[,3] == 'Olga' & permutaciones[,4] == 'Paty') | (permutaciones[,2] == 'Adriana' & permutaciones[,3] == 'Mary' & permutaciones[,4] == 'Olga' & permutaciones[,5] == 'Paty') | (permutaciones[,3] == 'Adriana' & permutaciones[,4] == 'Mary' & permutaciones[,5] == 'Olga' & permutaciones[,6] == 'Paty')),]

##       [,1]      [,2]      [,3]      [,4]   [,5]      [,6]     
##  [1,] "Abraham" "Adriana" "Mary"    "Olga" "Paty"    "Alexei" 
##  [2,] "Abraham" "Adriana" "Mary"    "Olga" "Paty"    "Caro"   
##  [3,] "Abraham" "Adriana" "Mary"    "Olga" "Paty"    "Jazhiel"
##  [4,] "Abraham" "Adriana" "Mary"    "Olga" "Paty"    "Jesus"  
##  [5,] "Abraham" "Adriana" "Mary"    "Olga" "Paty"    "Luis"   
##  [6,] "Abraham" "Alexei"  "Adriana" "Mary" "Olga"    "Paty"   
##  [7,] "Abraham" "Caro"    "Adriana" "Mary" "Olga"    "Paty"   
##  [8,] "Abraham" "Jazhiel" "Adriana" "Mary" "Olga"    "Paty"   
##  [9,] "Abraham" "Jesus"   "Adriana" "Mary" "Olga"    "Paty"   
## [10,] "Abraham" "Luis"    "Adriana" "Mary" "Olga"    "Paty"   
## [11,] "Adriana" "Mary"    "Olga"    "Paty" "Abraham" "Alexei" 
## [12,] "Adriana" "Mary"    "Olga"    "Paty" "Abraham" "Caro"   
## [13,] "Adriana" "Mary"    "Olga"    "Paty" "Abraham" "Jazhiel"
## [14,] "Adriana" "Mary"    "Olga"    "Paty" "Abraham" "Jesus"  
## [15,] "Adriana" "Mary"    "Olga"    "Paty" "Abraham" "Luis"   
## [16,] "Adriana" "Mary"    "Olga"    "Paty" "Alexei"  "Abraham"
## [17,] "Adriana" "Mary"    "Olga"    "Paty" "Alexei"  "Caro"   
## [18,] "Adriana" "Mary"    "Olga"    "Paty" "Alexei"  "Jazhiel"
## [19,] "Adriana" "Mary"    "Olga"    "Paty" "Alexei"  "Jesus"  
## [20,] "Adriana" "Mary"    "Olga"    "Paty" "Alexei"  "Luis"   
## [21,] "Adriana" "Mary"    "Olga"    "Paty" "Caro"    "Abraham"
## [22,] "Adriana" "Mary"    "Olga"    "Paty" "Caro"    "Alexei" 
## [23,] "Adriana" "Mary"    "Olga"    "Paty" "Caro"    "Jazhiel"
## [24,] "Adriana" "Mary"    "Olga"    "Paty" "Caro"    "Jesus"  
## [25,] "Adriana" "Mary"    "Olga"    "Paty" "Caro"    "Luis"   
## [26,] "Adriana" "Mary"    "Olga"    "Paty" "Jazhiel" "Abraham"
## [27,] "Adriana" "Mary"    "Olga"    "Paty" "Jazhiel" "Alexei" 
## [28,] "Adriana" "Mary"    "Olga"    "Paty" "Jazhiel" "Caro"   
## [29,] "Adriana" "Mary"    "Olga"    "Paty" "Jazhiel" "Jesus"  
## [30,] "Adriana" "Mary"    "Olga"    "Paty" "Jazhiel" "Luis"   
## [31,] "Adriana" "Mary"    "Olga"    "Paty" "Jesus"   "Abraham"
## [32,] "Adriana" "Mary"    "Olga"    "Paty" "Jesus"   "Alexei" 
## [33,] "Adriana" "Mary"    "Olga"    "Paty" "Jesus"   "Caro"   
## [34,] "Adriana" "Mary"    "Olga"    "Paty" "Jesus"   "Jazhiel"
## [35,] "Adriana" "Mary"    "Olga"    "Paty" "Jesus"   "Luis"   
## [36,] "Adriana" "Mary"    "Olga"    "Paty" "Luis"    "Abraham"
## [37,] "Adriana" "Mary"    "Olga"    "Paty" "Luis"    "Alexei" 
## [38,] "Adriana" "Mary"    "Olga"    "Paty" "Luis"    "Caro"   
## [39,] "Adriana" "Mary"    "Olga"    "Paty" "Luis"    "Jazhiel"
## [40,] "Adriana" "Mary"    "Olga"    "Paty" "Luis"    "Jesus"  
## [41,] "Alexei"  "Abraham" "Adriana" "Mary" "Olga"    "Paty"   
## [42,] "Alexei"  "Adriana" "Mary"    "Olga" "Paty"    "Abraham"
## [43,] "Alexei"  "Adriana" "Mary"    "Olga" "Paty"    "Caro"   
## [44,] "Alexei"  "Adriana" "Mary"    "Olga" "Paty"    "Jazhiel"
## [45,] "Alexei"  "Adriana" "Mary"    "Olga" "Paty"    "Jesus"  
## [46,] "Alexei"  "Adriana" "Mary"    "Olga" "Paty"    "Luis"   
## [47,] "Alexei"  "Caro"    "Adriana" "Mary" "Olga"    "Paty"   
## [48,] "Alexei"  "Jazhiel" "Adriana" "Mary" "Olga"    "Paty"   
## [49,] "Alexei"  "Jesus"   "Adriana" "Mary" "Olga"    "Paty"   
## [50,] "Alexei"  "Luis"    "Adriana" "Mary" "Olga"    "Paty"   
## [51,] "Caro"    "Abraham" "Adriana" "Mary" "Olga"    "Paty"   
## [52,] "Caro"    "Adriana" "Mary"    "Olga" "Paty"    "Abraham"
## [53,] "Caro"    "Adriana" "Mary"    "Olga" "Paty"    "Alexei" 
## [54,] "Caro"    "Adriana" "Mary"    "Olga" "Paty"    "Jazhiel"
## [55,] "Caro"    "Adriana" "Mary"    "Olga" "Paty"    "Jesus"  
## [56,] "Caro"    "Adriana" "Mary"    "Olga" "Paty"    "Luis"   
## [57,] "Caro"    "Alexei"  "Adriana" "Mary" "Olga"    "Paty"   
## [58,] "Caro"    "Jazhiel" "Adriana" "Mary" "Olga"    "Paty"   
## [59,] "Caro"    "Jesus"   "Adriana" "Mary" "Olga"    "Paty"   
## [60,] "Caro"    "Luis"    "Adriana" "Mary" "Olga"    "Paty"   
## [61,] "Jazhiel" "Abraham" "Adriana" "Mary" "Olga"    "Paty"   
## [62,] "Jazhiel" "Adriana" "Mary"    "Olga" "Paty"    "Abraham"
## [63,] "Jazhiel" "Adriana" "Mary"    "Olga" "Paty"    "Alexei" 
## [64,] "Jazhiel" "Adriana" "Mary"    "Olga" "Paty"    "Caro"   
## [65,] "Jazhiel" "Adriana" "Mary"    "Olga" "Paty"    "Jesus"  
## [66,] "Jazhiel" "Adriana" "Mary"    "Olga" "Paty"    "Luis"   
## [67,] "Jazhiel" "Alexei"  "Adriana" "Mary" "Olga"    "Paty"   
## [68,] "Jazhiel" "Caro"    "Adriana" "Mary" "Olga"    "Paty"   
## [69,] "Jazhiel" "Jesus"   "Adriana" "Mary" "Olga"    "Paty"   
## [70,] "Jazhiel" "Luis"    "Adriana" "Mary" "Olga"    "Paty"   
## [71,] "Jesus"   "Abraham" "Adriana" "Mary" "Olga"    "Paty"   
## [72,] "Jesus"   "Adriana" "Mary"    "Olga" "Paty"    "Abraham"
## [73,] "Jesus"   "Adriana" "Mary"    "Olga" "Paty"    "Alexei" 
## [74,] "Jesus"   "Adriana" "Mary"    "Olga" "Paty"    "Caro"   
## [75,] "Jesus"   "Adriana" "Mary"    "Olga" "Paty"    "Jazhiel"
## [76,] "Jesus"   "Adriana" "Mary"    "Olga" "Paty"    "Luis"   
## [77,] "Jesus"   "Alexei"  "Adriana" "Mary" "Olga"    "Paty"   
## [78,] "Jesus"   "Caro"    "Adriana" "Mary" "Olga"    "Paty"   
## [79,] "Jesus"   "Jazhiel" "Adriana" "Mary" "Olga"    "Paty"   
## [80,] "Jesus"   "Luis"    "Adriana" "Mary" "Olga"    "Paty"   
## [81,] "Luis"    "Abraham" "Adriana" "Mary" "Olga"    "Paty"   
## [82,] "Luis"    "Adriana" "Mary"    "Olga" "Paty"    "Abraham"
## [83,] "Luis"    "Adriana" "Mary"    "Olga" "Paty"    "Alexei" 
## [84,] "Luis"    "Adriana" "Mary"    "Olga" "Paty"    "Caro"   
## [85,] "Luis"    "Adriana" "Mary"    "Olga" "Paty"    "Jazhiel"
## [86,] "Luis"    "Adriana" "Mary"    "Olga" "Paty"    "Jesus"  
## [87,] "Luis"    "Alexei"  "Adriana" "Mary" "Olga"    "Paty"   
## [88,] "Luis"    "Caro"    "Adriana" "Mary" "Olga"    "Paty"   
## [89,] "Luis"    "Jazhiel" "Adriana" "Mary" "Olga"    "Paty"   
## [90,] "Luis"    "Jesus"   "Adriana" "Mary" "Olga"    "Paty"

Practica6: Combinaciones y Permutaciones mediante R

19041245 Luis Fernando Rivera Morales

11 de marzo de 2020

Importar la libreria

Los datos y datos ordenados

Combinaciones en grupos de 2

¿Cuantas combinaciones salen?

Comprobacion conforme a la formula

Permutaciones con grupos de 2

¿Cuantas permutaciones salen?

Comprobar mediante la formula

Combinaciones grupos de 4

Comprobar mediante la formula

permutaciones con grupos de 4

¿Cuantas permutaciones salen?

Comprobar mediante la formula

Combinaciones con grupos de 6

¿Cuantas combinaciones salen?

Comprobacion mediante la formula

Permutaciones con grupos de 6

Comprobar conforme a la fórmula

Analizando datos con COMBINACIONES de grupos de 6

Pregunta 9 ¿En cuántas combinaciones de grupos seis está ‘Adriana’ en la primera columna?.

Pregunta 10: ¿En cuántas combinaciones de grupos seis está ‘Adriana’ en la primera o en la segunda o en la tercera columna?

Pregunta 11: ¿En cuántas combinaciones de grupos seis está ‘Paty’ en la cuarta o en la quinta o en la sexta columna?

Pregunta 12: ¿En cuántas combinaciones de grupos seis está ‘Olga’ en la cuarta o en la quinta o en la sexta columna?

Pregunta 13: ¿En cuántas combinaciones de grupos seis está ‘Olga’ en cualquier columna de la 1 a la 6?

Pregunta 14: ¿En cuántas combinaciones de grupos seis están ‘Adriana’, ‘Mary’, ‘Olga’ y ‘Paty’ en cualquier columna de la 1 a la 6. Deben de estar ellas, en cuáles y cuántas aparecen?

Pregunta 15: ¿En cuántas permutaciones de grupos seis está ‘Adriana’ en la primera o en la segunda o en la tercera columna?

Pregunta 16: ¿En cuántas permutaciones de grupos seis está ‘Paty’ en la cuarta o en la quinta o en la sexta columna?.

Pregunta 17: ¿En cuántas permutaciones de grupos seis está ‘Olga’ en la cuarta o en la quinta o en la sexta columna?.

Pregunta 18: ¿En cuántas permutaciones de grupos seis está ‘Olga’ en cualquier columna de la 1 a la 6?

Pregunta 19: ¿En cuántas permutaciones de grupos seis están ‘Adriana’, ‘Mary’, ‘Olga’ y ‘Paty’ en cualquier columna de la 1 a la 6. Deben de estar ellas, en cuáles y cuántas aparecen?.

Pregunta 20: ¿En cuantas ocasiones de las PERMUTACIONES en grupos de SEIS se encuentra juntas “Adriana”, “Mary”, “Olga” y “Paty”. Ya sean en las columnas 1-4, o en las columnas 2-5, o en las columnas 3-6. en ese orden?.