Equipo:
Jesus Ruiz Tinajero
No de Control: 19041250
Angel Rafael Olivas Garcia
No de Control: 19041232
Oscar Ivan Alonso Simental
No de Control: 19041186
Juan Manuel Salcido Ruelas
No de Control: 19041252
Objetivo: Realizar combinaciones y permutaciones dado un conjunto de nombres de personas. Se determinan las combinaciones y permutaciones con grupos de 2 4 y 6 identificando la cantidad de opciones generadas.
1. Lista de un conjunto de 10 nombre que debe incluir entre ellos a “Adriana”, “Mary”, “Olga” y “Paty”
library(gtools)
nombres <- c("Ahri", "Alonso", "Angel", "Juan", "Augustus", "Jesus", "Paty", "Adriana", "Olga", "Mary")
2. Ordenar el conjunto de nombres y mostrar en pantalla. Los nombres deberán ser los integrantes de los equipos.
nombres <- sort(nombres)
nombres
## [1] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Jesus"
## [7] "Juan" "Mary" "Olga" "Paty"
3. Determinar combinaciones del conjunto de nombres en grupos de 2 identificar cuáles y cuántas combinaciones hay? Visualizar.
N <- length(nombres) # Cantidad de alumnos
n <- 2 # Grupos de 2
combinaciones <- combinations(N, n, nombres)
head(combinaciones)
## [,1] [,2]
## [1,] "Adriana" "Ahri"
## [2,] "Adriana" "Alonso"
## [3,] "Adriana" "Angel"
## [4,] "Adriana" "Augustus"
## [5,] "Adriana" "Jesus"
## [6,] "Adriana" "Juan"
# cuantas salen
nrow(combinaciones) # ¿cuántas combinaciones?
## [1] 45
# Comprobar conforme a la fórmula
factorial(N) / (factorial(n) * (factorial (N-n)))
## [1] 45
4. Determinar combinaciones del conjunto de nombres en grupos de 4, identificar cuáles y cuántas combinaciones hay? Visualizar.
N <- length(nombres) # Cantidad de alumnos
n <- 4 # Grupos de 4
combinaciones <- combinations(N, n, nombres)
head(combinaciones)
## [,1] [,2] [,3] [,4]
## [1,] "Adriana" "Ahri" "Alonso" "Angel"
## [2,] "Adriana" "Ahri" "Alonso" "Augustus"
## [3,] "Adriana" "Ahri" "Alonso" "Jesus"
## [4,] "Adriana" "Ahri" "Alonso" "Juan"
## [5,] "Adriana" "Ahri" "Alonso" "Mary"
## [6,] "Adriana" "Ahri" "Alonso" "Olga"
# cuantas salen
nrow(combinaciones) # ¿cuántas combinaciones?
## [1] 210
# Comprobar conforme a la fórmula
factorial(N) / (factorial(n) * (factorial (N-n)))
## [1] 210
5. Determinar combinaciones del conjunto de nombres en grupos de 6, identificar cuáles y cuántas combinaciones hay? Visualizar.
N <- length(nombres) # Cantidad de alumnos
n <- 6 # Grupos de 6
combinaciones <- combinations(N, n, nombres)
head(combinaciones)
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Jesus"
## [2,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Juan"
## [3,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Mary"
## [4,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Olga"
## [5,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Paty"
## [6,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Juan"
# Comprobar conforme a la fórmula
factorial(N) / (factorial(n) * (factorial (N-n)))
## [1] 210
6. Determinar permutaciones del conjunto de nombres en grupos de 2 identificar cuáles y cuántas combinaciones hay? Visualizar.
N <- length(nombres) # Cantidad de alumnos
n <- 2 # Grupos de 2
permutaciones <- permutations(N, n, nombres)
head(permutaciones)
## [,1] [,2]
## [1,] "Adriana" "Ahri"
## [2,] "Adriana" "Alonso"
## [3,] "Adriana" "Angel"
## [4,] "Adriana" "Augustus"
## [5,] "Adriana" "Jesus"
## [6,] "Adriana" "Juan"
# cuantas salen
nrow(permutaciones) # ¿cuántas permutaciones?
## [1] 90
# Comprobar conforme a la fórmula
factorial(N) / (factorial (N-n))
## [1] 90
7. Determinar permutaciones del conjunto de nombres en grupos de 4, identificar cuáles y cuántas combinaciones hay? Visualizar.
N <- length(nombres) # Cantidad de alumnos
n <- 4 # Grupos de 4
permutaciones <- permutations(N, n, nombres)
head(permutaciones)
## [,1] [,2] [,3] [,4]
## [1,] "Adriana" "Ahri" "Alonso" "Angel"
## [2,] "Adriana" "Ahri" "Alonso" "Augustus"
## [3,] "Adriana" "Ahri" "Alonso" "Jesus"
## [4,] "Adriana" "Ahri" "Alonso" "Juan"
## [5,] "Adriana" "Ahri" "Alonso" "Mary"
## [6,] "Adriana" "Ahri" "Alonso" "Olga"
# cuantas salen
nrow(permutaciones) # ¿cuántas permutaciones?
## [1] 5040
# Comprobar conforme a la fórmula
factorial(N) / (factorial (N-n))
## [1] 5040
8. Determinar permutacionesdel conjunto de nombres en grupos de 6, identificar cuáles y cuántas combinaciones hay? Visualizar.
N <- length(nombres) # Cantidad de alumnos
n <- 6 # Grupos de 6
permutaciones <- permutations(N, n, nombres)
head(permutaciones)
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Jesus"
## [2,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Juan"
## [3,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Mary"
## [4,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Olga"
## [5,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Paty"
## [6,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Augustus"
# cuantas salen
nrow(permutaciones) # ¿cuántas permutaciones?
## [1] 151200
# Comprobar conforme a la fórmula
factorial(N) / (factorial (N-n))
## [1] 151200
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" "Ahri" "Alonso" "Angel" "Augustus" "Jesus"
## [2,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Juan"
## [3,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Mary"
## [4,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Olga"
## [5,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Paty"
## [6,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Juan"
## [7,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Mary"
## [8,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Olga"
## [9,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Paty"
## [10,] "Adriana" "Ahri" "Alonso" "Angel" "Juan" "Mary"
## [11,] "Adriana" "Ahri" "Alonso" "Angel" "Juan" "Olga"
## [12,] "Adriana" "Ahri" "Alonso" "Angel" "Juan" "Paty"
## [13,] "Adriana" "Ahri" "Alonso" "Angel" "Mary" "Olga"
## [14,] "Adriana" "Ahri" "Alonso" "Angel" "Mary" "Paty"
## [15,] "Adriana" "Ahri" "Alonso" "Angel" "Olga" "Paty"
## [16,] "Adriana" "Ahri" "Alonso" "Augustus" "Jesus" "Juan"
## [17,] "Adriana" "Ahri" "Alonso" "Augustus" "Jesus" "Mary"
## [18,] "Adriana" "Ahri" "Alonso" "Augustus" "Jesus" "Olga"
## [19,] "Adriana" "Ahri" "Alonso" "Augustus" "Jesus" "Paty"
## [20,] "Adriana" "Ahri" "Alonso" "Augustus" "Juan" "Mary"
## [21,] "Adriana" "Ahri" "Alonso" "Augustus" "Juan" "Olga"
## [22,] "Adriana" "Ahri" "Alonso" "Augustus" "Juan" "Paty"
## [23,] "Adriana" "Ahri" "Alonso" "Augustus" "Mary" "Olga"
## [24,] "Adriana" "Ahri" "Alonso" "Augustus" "Mary" "Paty"
## [25,] "Adriana" "Ahri" "Alonso" "Augustus" "Olga" "Paty"
## [26,] "Adriana" "Ahri" "Alonso" "Jesus" "Juan" "Mary"
## [27,] "Adriana" "Ahri" "Alonso" "Jesus" "Juan" "Olga"
## [28,] "Adriana" "Ahri" "Alonso" "Jesus" "Juan" "Paty"
## [29,] "Adriana" "Ahri" "Alonso" "Jesus" "Mary" "Olga"
## [30,] "Adriana" "Ahri" "Alonso" "Jesus" "Mary" "Paty"
## [31,] "Adriana" "Ahri" "Alonso" "Jesus" "Olga" "Paty"
## [32,] "Adriana" "Ahri" "Alonso" "Juan" "Mary" "Olga"
## [33,] "Adriana" "Ahri" "Alonso" "Juan" "Mary" "Paty"
## [34,] "Adriana" "Ahri" "Alonso" "Juan" "Olga" "Paty"
## [35,] "Adriana" "Ahri" "Alonso" "Mary" "Olga" "Paty"
## [36,] "Adriana" "Ahri" "Angel" "Augustus" "Jesus" "Juan"
## [37,] "Adriana" "Ahri" "Angel" "Augustus" "Jesus" "Mary"
## [38,] "Adriana" "Ahri" "Angel" "Augustus" "Jesus" "Olga"
## [39,] "Adriana" "Ahri" "Angel" "Augustus" "Jesus" "Paty"
## [40,] "Adriana" "Ahri" "Angel" "Augustus" "Juan" "Mary"
## [41,] "Adriana" "Ahri" "Angel" "Augustus" "Juan" "Olga"
## [42,] "Adriana" "Ahri" "Angel" "Augustus" "Juan" "Paty"
## [43,] "Adriana" "Ahri" "Angel" "Augustus" "Mary" "Olga"
## [44,] "Adriana" "Ahri" "Angel" "Augustus" "Mary" "Paty"
## [45,] "Adriana" "Ahri" "Angel" "Augustus" "Olga" "Paty"
## [46,] "Adriana" "Ahri" "Angel" "Jesus" "Juan" "Mary"
## [47,] "Adriana" "Ahri" "Angel" "Jesus" "Juan" "Olga"
## [48,] "Adriana" "Ahri" "Angel" "Jesus" "Juan" "Paty"
## [49,] "Adriana" "Ahri" "Angel" "Jesus" "Mary" "Olga"
## [50,] "Adriana" "Ahri" "Angel" "Jesus" "Mary" "Paty"
## [51,] "Adriana" "Ahri" "Angel" "Jesus" "Olga" "Paty"
## [52,] "Adriana" "Ahri" "Angel" "Juan" "Mary" "Olga"
## [53,] "Adriana" "Ahri" "Angel" "Juan" "Mary" "Paty"
## [54,] "Adriana" "Ahri" "Angel" "Juan" "Olga" "Paty"
## [55,] "Adriana" "Ahri" "Angel" "Mary" "Olga" "Paty"
## [56,] "Adriana" "Ahri" "Augustus" "Jesus" "Juan" "Mary"
## [57,] "Adriana" "Ahri" "Augustus" "Jesus" "Juan" "Olga"
## [58,] "Adriana" "Ahri" "Augustus" "Jesus" "Juan" "Paty"
## [59,] "Adriana" "Ahri" "Augustus" "Jesus" "Mary" "Olga"
## [60,] "Adriana" "Ahri" "Augustus" "Jesus" "Mary" "Paty"
## [61,] "Adriana" "Ahri" "Augustus" "Jesus" "Olga" "Paty"
## [62,] "Adriana" "Ahri" "Augustus" "Juan" "Mary" "Olga"
## [63,] "Adriana" "Ahri" "Augustus" "Juan" "Mary" "Paty"
## [64,] "Adriana" "Ahri" "Augustus" "Juan" "Olga" "Paty"
## [65,] "Adriana" "Ahri" "Augustus" "Mary" "Olga" "Paty"
## [66,] "Adriana" "Ahri" "Jesus" "Juan" "Mary" "Olga"
## [67,] "Adriana" "Ahri" "Jesus" "Juan" "Mary" "Paty"
## [68,] "Adriana" "Ahri" "Jesus" "Juan" "Olga" "Paty"
## [69,] "Adriana" "Ahri" "Jesus" "Mary" "Olga" "Paty"
## [70,] "Adriana" "Ahri" "Juan" "Mary" "Olga" "Paty"
## [71,] "Adriana" "Alonso" "Angel" "Augustus" "Jesus" "Juan"
## [72,] "Adriana" "Alonso" "Angel" "Augustus" "Jesus" "Mary"
## [73,] "Adriana" "Alonso" "Angel" "Augustus" "Jesus" "Olga"
## [74,] "Adriana" "Alonso" "Angel" "Augustus" "Jesus" "Paty"
## [75,] "Adriana" "Alonso" "Angel" "Augustus" "Juan" "Mary"
## [76,] "Adriana" "Alonso" "Angel" "Augustus" "Juan" "Olga"
## [77,] "Adriana" "Alonso" "Angel" "Augustus" "Juan" "Paty"
## [78,] "Adriana" "Alonso" "Angel" "Augustus" "Mary" "Olga"
## [79,] "Adriana" "Alonso" "Angel" "Augustus" "Mary" "Paty"
## [80,] "Adriana" "Alonso" "Angel" "Augustus" "Olga" "Paty"
## [81,] "Adriana" "Alonso" "Angel" "Jesus" "Juan" "Mary"
## [82,] "Adriana" "Alonso" "Angel" "Jesus" "Juan" "Olga"
## [83,] "Adriana" "Alonso" "Angel" "Jesus" "Juan" "Paty"
## [84,] "Adriana" "Alonso" "Angel" "Jesus" "Mary" "Olga"
## [85,] "Adriana" "Alonso" "Angel" "Jesus" "Mary" "Paty"
## [86,] "Adriana" "Alonso" "Angel" "Jesus" "Olga" "Paty"
## [87,] "Adriana" "Alonso" "Angel" "Juan" "Mary" "Olga"
## [88,] "Adriana" "Alonso" "Angel" "Juan" "Mary" "Paty"
## [89,] "Adriana" "Alonso" "Angel" "Juan" "Olga" "Paty"
## [90,] "Adriana" "Alonso" "Angel" "Mary" "Olga" "Paty"
## [91,] "Adriana" "Alonso" "Augustus" "Jesus" "Juan" "Mary"
## [92,] "Adriana" "Alonso" "Augustus" "Jesus" "Juan" "Olga"
## [93,] "Adriana" "Alonso" "Augustus" "Jesus" "Juan" "Paty"
## [94,] "Adriana" "Alonso" "Augustus" "Jesus" "Mary" "Olga"
## [95,] "Adriana" "Alonso" "Augustus" "Jesus" "Mary" "Paty"
## [96,] "Adriana" "Alonso" "Augustus" "Jesus" "Olga" "Paty"
## [97,] "Adriana" "Alonso" "Augustus" "Juan" "Mary" "Olga"
## [98,] "Adriana" "Alonso" "Augustus" "Juan" "Mary" "Paty"
## [99,] "Adriana" "Alonso" "Augustus" "Juan" "Olga" "Paty"
## [100,] "Adriana" "Alonso" "Augustus" "Mary" "Olga" "Paty"
## [101,] "Adriana" "Alonso" "Jesus" "Juan" "Mary" "Olga"
## [102,] "Adriana" "Alonso" "Jesus" "Juan" "Mary" "Paty"
## [103,] "Adriana" "Alonso" "Jesus" "Juan" "Olga" "Paty"
## [104,] "Adriana" "Alonso" "Jesus" "Mary" "Olga" "Paty"
## [105,] "Adriana" "Alonso" "Juan" "Mary" "Olga" "Paty"
## [106,] "Adriana" "Angel" "Augustus" "Jesus" "Juan" "Mary"
## [107,] "Adriana" "Angel" "Augustus" "Jesus" "Juan" "Olga"
## [108,] "Adriana" "Angel" "Augustus" "Jesus" "Juan" "Paty"
## [109,] "Adriana" "Angel" "Augustus" "Jesus" "Mary" "Olga"
## [110,] "Adriana" "Angel" "Augustus" "Jesus" "Mary" "Paty"
## [111,] "Adriana" "Angel" "Augustus" "Jesus" "Olga" "Paty"
## [112,] "Adriana" "Angel" "Augustus" "Juan" "Mary" "Olga"
## [113,] "Adriana" "Angel" "Augustus" "Juan" "Mary" "Paty"
## [114,] "Adriana" "Angel" "Augustus" "Juan" "Olga" "Paty"
## [115,] "Adriana" "Angel" "Augustus" "Mary" "Olga" "Paty"
## [116,] "Adriana" "Angel" "Jesus" "Juan" "Mary" "Olga"
## [117,] "Adriana" "Angel" "Jesus" "Juan" "Mary" "Paty"
## [118,] "Adriana" "Angel" "Jesus" "Juan" "Olga" "Paty"
## [119,] "Adriana" "Angel" "Jesus" "Mary" "Olga" "Paty"
## [120,] "Adriana" "Angel" "Juan" "Mary" "Olga" "Paty"
## [121,] "Adriana" "Augustus" "Jesus" "Juan" "Mary" "Olga"
## [122,] "Adriana" "Augustus" "Jesus" "Juan" "Mary" "Paty"
## [123,] "Adriana" "Augustus" "Jesus" "Juan" "Olga" "Paty"
## [124,] "Adriana" "Augustus" "Jesus" "Mary" "Olga" "Paty"
## [125,] "Adriana" "Augustus" "Juan" "Mary" "Olga" "Paty"
## [126,] "Adriana" "Jesus" "Juan" "Mary" "Olga" "Paty"
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,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Jesus"
## [2,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Juan"
## [3,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Mary"
## [4,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Olga"
## [5,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Paty"
## [6,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Juan"
## [7,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Mary"
## [8,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Olga"
## [9,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Paty"
## [10,] "Adriana" "Ahri" "Alonso" "Angel" "Juan" "Mary"
## [11,] "Adriana" "Ahri" "Alonso" "Angel" "Juan" "Olga"
## [12,] "Adriana" "Ahri" "Alonso" "Angel" "Juan" "Paty"
## [13,] "Adriana" "Ahri" "Alonso" "Angel" "Mary" "Olga"
## [14,] "Adriana" "Ahri" "Alonso" "Angel" "Mary" "Paty"
## [15,] "Adriana" "Ahri" "Alonso" "Angel" "Olga" "Paty"
## [16,] "Adriana" "Ahri" "Alonso" "Augustus" "Jesus" "Juan"
## [17,] "Adriana" "Ahri" "Alonso" "Augustus" "Jesus" "Mary"
## [18,] "Adriana" "Ahri" "Alonso" "Augustus" "Jesus" "Olga"
## [19,] "Adriana" "Ahri" "Alonso" "Augustus" "Jesus" "Paty"
## [20,] "Adriana" "Ahri" "Alonso" "Augustus" "Juan" "Mary"
## [21,] "Adriana" "Ahri" "Alonso" "Augustus" "Juan" "Olga"
## [22,] "Adriana" "Ahri" "Alonso" "Augustus" "Juan" "Paty"
## [23,] "Adriana" "Ahri" "Alonso" "Augustus" "Mary" "Olga"
## [24,] "Adriana" "Ahri" "Alonso" "Augustus" "Mary" "Paty"
## [25,] "Adriana" "Ahri" "Alonso" "Augustus" "Olga" "Paty"
## [26,] "Adriana" "Ahri" "Alonso" "Jesus" "Juan" "Mary"
## [27,] "Adriana" "Ahri" "Alonso" "Jesus" "Juan" "Olga"
## [28,] "Adriana" "Ahri" "Alonso" "Jesus" "Juan" "Paty"
## [29,] "Adriana" "Ahri" "Alonso" "Jesus" "Mary" "Olga"
## [30,] "Adriana" "Ahri" "Alonso" "Jesus" "Mary" "Paty"
## [31,] "Adriana" "Ahri" "Alonso" "Jesus" "Olga" "Paty"
## [32,] "Adriana" "Ahri" "Alonso" "Juan" "Mary" "Olga"
## [33,] "Adriana" "Ahri" "Alonso" "Juan" "Mary" "Paty"
## [34,] "Adriana" "Ahri" "Alonso" "Juan" "Olga" "Paty"
## [35,] "Adriana" "Ahri" "Alonso" "Mary" "Olga" "Paty"
## [36,] "Adriana" "Ahri" "Angel" "Augustus" "Jesus" "Juan"
## [37,] "Adriana" "Ahri" "Angel" "Augustus" "Jesus" "Mary"
## [38,] "Adriana" "Ahri" "Angel" "Augustus" "Jesus" "Olga"
## [39,] "Adriana" "Ahri" "Angel" "Augustus" "Jesus" "Paty"
## [40,] "Adriana" "Ahri" "Angel" "Augustus" "Juan" "Mary"
## [41,] "Adriana" "Ahri" "Angel" "Augustus" "Juan" "Olga"
## [42,] "Adriana" "Ahri" "Angel" "Augustus" "Juan" "Paty"
## [43,] "Adriana" "Ahri" "Angel" "Augustus" "Mary" "Olga"
## [44,] "Adriana" "Ahri" "Angel" "Augustus" "Mary" "Paty"
## [45,] "Adriana" "Ahri" "Angel" "Augustus" "Olga" "Paty"
## [46,] "Adriana" "Ahri" "Angel" "Jesus" "Juan" "Mary"
## [47,] "Adriana" "Ahri" "Angel" "Jesus" "Juan" "Olga"
## [48,] "Adriana" "Ahri" "Angel" "Jesus" "Juan" "Paty"
## [49,] "Adriana" "Ahri" "Angel" "Jesus" "Mary" "Olga"
## [50,] "Adriana" "Ahri" "Angel" "Jesus" "Mary" "Paty"
## [51,] "Adriana" "Ahri" "Angel" "Jesus" "Olga" "Paty"
## [52,] "Adriana" "Ahri" "Angel" "Juan" "Mary" "Olga"
## [53,] "Adriana" "Ahri" "Angel" "Juan" "Mary" "Paty"
## [54,] "Adriana" "Ahri" "Angel" "Juan" "Olga" "Paty"
## [55,] "Adriana" "Ahri" "Angel" "Mary" "Olga" "Paty"
## [56,] "Adriana" "Ahri" "Augustus" "Jesus" "Juan" "Mary"
## [57,] "Adriana" "Ahri" "Augustus" "Jesus" "Juan" "Olga"
## [58,] "Adriana" "Ahri" "Augustus" "Jesus" "Juan" "Paty"
## [59,] "Adriana" "Ahri" "Augustus" "Jesus" "Mary" "Olga"
## [60,] "Adriana" "Ahri" "Augustus" "Jesus" "Mary" "Paty"
## [61,] "Adriana" "Ahri" "Augustus" "Jesus" "Olga" "Paty"
## [62,] "Adriana" "Ahri" "Augustus" "Juan" "Mary" "Olga"
## [63,] "Adriana" "Ahri" "Augustus" "Juan" "Mary" "Paty"
## [64,] "Adriana" "Ahri" "Augustus" "Juan" "Olga" "Paty"
## [65,] "Adriana" "Ahri" "Augustus" "Mary" "Olga" "Paty"
## [66,] "Adriana" "Ahri" "Jesus" "Juan" "Mary" "Olga"
## [67,] "Adriana" "Ahri" "Jesus" "Juan" "Mary" "Paty"
## [68,] "Adriana" "Ahri" "Jesus" "Juan" "Olga" "Paty"
## [69,] "Adriana" "Ahri" "Jesus" "Mary" "Olga" "Paty"
## [70,] "Adriana" "Ahri" "Juan" "Mary" "Olga" "Paty"
## [71,] "Adriana" "Alonso" "Angel" "Augustus" "Jesus" "Juan"
## [72,] "Adriana" "Alonso" "Angel" "Augustus" "Jesus" "Mary"
## [73,] "Adriana" "Alonso" "Angel" "Augustus" "Jesus" "Olga"
## [74,] "Adriana" "Alonso" "Angel" "Augustus" "Jesus" "Paty"
## [75,] "Adriana" "Alonso" "Angel" "Augustus" "Juan" "Mary"
## [76,] "Adriana" "Alonso" "Angel" "Augustus" "Juan" "Olga"
## [77,] "Adriana" "Alonso" "Angel" "Augustus" "Juan" "Paty"
## [78,] "Adriana" "Alonso" "Angel" "Augustus" "Mary" "Olga"
## [79,] "Adriana" "Alonso" "Angel" "Augustus" "Mary" "Paty"
## [80,] "Adriana" "Alonso" "Angel" "Augustus" "Olga" "Paty"
## [81,] "Adriana" "Alonso" "Angel" "Jesus" "Juan" "Mary"
## [82,] "Adriana" "Alonso" "Angel" "Jesus" "Juan" "Olga"
## [83,] "Adriana" "Alonso" "Angel" "Jesus" "Juan" "Paty"
## [84,] "Adriana" "Alonso" "Angel" "Jesus" "Mary" "Olga"
## [85,] "Adriana" "Alonso" "Angel" "Jesus" "Mary" "Paty"
## [86,] "Adriana" "Alonso" "Angel" "Jesus" "Olga" "Paty"
## [87,] "Adriana" "Alonso" "Angel" "Juan" "Mary" "Olga"
## [88,] "Adriana" "Alonso" "Angel" "Juan" "Mary" "Paty"
## [89,] "Adriana" "Alonso" "Angel" "Juan" "Olga" "Paty"
## [90,] "Adriana" "Alonso" "Angel" "Mary" "Olga" "Paty"
## [91,] "Adriana" "Alonso" "Augustus" "Jesus" "Juan" "Mary"
## [92,] "Adriana" "Alonso" "Augustus" "Jesus" "Juan" "Olga"
## [93,] "Adriana" "Alonso" "Augustus" "Jesus" "Juan" "Paty"
## [94,] "Adriana" "Alonso" "Augustus" "Jesus" "Mary" "Olga"
## [95,] "Adriana" "Alonso" "Augustus" "Jesus" "Mary" "Paty"
## [96,] "Adriana" "Alonso" "Augustus" "Jesus" "Olga" "Paty"
## [97,] "Adriana" "Alonso" "Augustus" "Juan" "Mary" "Olga"
## [98,] "Adriana" "Alonso" "Augustus" "Juan" "Mary" "Paty"
## [99,] "Adriana" "Alonso" "Augustus" "Juan" "Olga" "Paty"
## [100,] "Adriana" "Alonso" "Augustus" "Mary" "Olga" "Paty"
## [101,] "Adriana" "Alonso" "Jesus" "Juan" "Mary" "Olga"
## [102,] "Adriana" "Alonso" "Jesus" "Juan" "Mary" "Paty"
## [103,] "Adriana" "Alonso" "Jesus" "Juan" "Olga" "Paty"
## [104,] "Adriana" "Alonso" "Jesus" "Mary" "Olga" "Paty"
## [105,] "Adriana" "Alonso" "Juan" "Mary" "Olga" "Paty"
## [106,] "Adriana" "Angel" "Augustus" "Jesus" "Juan" "Mary"
## [107,] "Adriana" "Angel" "Augustus" "Jesus" "Juan" "Olga"
## [108,] "Adriana" "Angel" "Augustus" "Jesus" "Juan" "Paty"
## [109,] "Adriana" "Angel" "Augustus" "Jesus" "Mary" "Olga"
## [110,] "Adriana" "Angel" "Augustus" "Jesus" "Mary" "Paty"
## [111,] "Adriana" "Angel" "Augustus" "Jesus" "Olga" "Paty"
## [112,] "Adriana" "Angel" "Augustus" "Juan" "Mary" "Olga"
## [113,] "Adriana" "Angel" "Augustus" "Juan" "Mary" "Paty"
## [114,] "Adriana" "Angel" "Augustus" "Juan" "Olga" "Paty"
## [115,] "Adriana" "Angel" "Augustus" "Mary" "Olga" "Paty"
## [116,] "Adriana" "Angel" "Jesus" "Juan" "Mary" "Olga"
## [117,] "Adriana" "Angel" "Jesus" "Juan" "Mary" "Paty"
## [118,] "Adriana" "Angel" "Jesus" "Juan" "Olga" "Paty"
## [119,] "Adriana" "Angel" "Jesus" "Mary" "Olga" "Paty"
## [120,] "Adriana" "Angel" "Juan" "Mary" "Olga" "Paty"
## [121,] "Adriana" "Augustus" "Jesus" "Juan" "Mary" "Olga"
## [122,] "Adriana" "Augustus" "Jesus" "Juan" "Mary" "Paty"
## [123,] "Adriana" "Augustus" "Jesus" "Juan" "Olga" "Paty"
## [124,] "Adriana" "Augustus" "Jesus" "Mary" "Olga" "Paty"
## [125,] "Adriana" "Augustus" "Juan" "Mary" "Olga" "Paty"
## [126,] "Adriana" "Jesus" "Juan" "Mary" "Olga" "Paty"
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,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Paty"
## [2,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Paty"
## [3,] "Adriana" "Ahri" "Alonso" "Angel" "Juan" "Paty"
## [4,] "Adriana" "Ahri" "Alonso" "Angel" "Mary" "Paty"
## [5,] "Adriana" "Ahri" "Alonso" "Angel" "Olga" "Paty"
## [6,] "Adriana" "Ahri" "Alonso" "Augustus" "Jesus" "Paty"
## [7,] "Adriana" "Ahri" "Alonso" "Augustus" "Juan" "Paty"
## [8,] "Adriana" "Ahri" "Alonso" "Augustus" "Mary" "Paty"
## [9,] "Adriana" "Ahri" "Alonso" "Augustus" "Olga" "Paty"
## [10,] "Adriana" "Ahri" "Alonso" "Jesus" "Juan" "Paty"
## [11,] "Adriana" "Ahri" "Alonso" "Jesus" "Mary" "Paty"
## [12,] "Adriana" "Ahri" "Alonso" "Jesus" "Olga" "Paty"
## [13,] "Adriana" "Ahri" "Alonso" "Juan" "Mary" "Paty"
## [14,] "Adriana" "Ahri" "Alonso" "Juan" "Olga" "Paty"
## [15,] "Adriana" "Ahri" "Alonso" "Mary" "Olga" "Paty"
## [16,] "Adriana" "Ahri" "Angel" "Augustus" "Jesus" "Paty"
## [17,] "Adriana" "Ahri" "Angel" "Augustus" "Juan" "Paty"
## [18,] "Adriana" "Ahri" "Angel" "Augustus" "Mary" "Paty"
## [19,] "Adriana" "Ahri" "Angel" "Augustus" "Olga" "Paty"
## [20,] "Adriana" "Ahri" "Angel" "Jesus" "Juan" "Paty"
## [21,] "Adriana" "Ahri" "Angel" "Jesus" "Mary" "Paty"
## [22,] "Adriana" "Ahri" "Angel" "Jesus" "Olga" "Paty"
## [23,] "Adriana" "Ahri" "Angel" "Juan" "Mary" "Paty"
## [24,] "Adriana" "Ahri" "Angel" "Juan" "Olga" "Paty"
## [25,] "Adriana" "Ahri" "Angel" "Mary" "Olga" "Paty"
## [26,] "Adriana" "Ahri" "Augustus" "Jesus" "Juan" "Paty"
## [27,] "Adriana" "Ahri" "Augustus" "Jesus" "Mary" "Paty"
## [28,] "Adriana" "Ahri" "Augustus" "Jesus" "Olga" "Paty"
## [29,] "Adriana" "Ahri" "Augustus" "Juan" "Mary" "Paty"
## [30,] "Adriana" "Ahri" "Augustus" "Juan" "Olga" "Paty"
## [31,] "Adriana" "Ahri" "Augustus" "Mary" "Olga" "Paty"
## [32,] "Adriana" "Ahri" "Jesus" "Juan" "Mary" "Paty"
## [33,] "Adriana" "Ahri" "Jesus" "Juan" "Olga" "Paty"
## [34,] "Adriana" "Ahri" "Jesus" "Mary" "Olga" "Paty"
## [35,] "Adriana" "Ahri" "Juan" "Mary" "Olga" "Paty"
## [36,] "Adriana" "Alonso" "Angel" "Augustus" "Jesus" "Paty"
## [37,] "Adriana" "Alonso" "Angel" "Augustus" "Juan" "Paty"
## [38,] "Adriana" "Alonso" "Angel" "Augustus" "Mary" "Paty"
## [39,] "Adriana" "Alonso" "Angel" "Augustus" "Olga" "Paty"
## [40,] "Adriana" "Alonso" "Angel" "Jesus" "Juan" "Paty"
## [41,] "Adriana" "Alonso" "Angel" "Jesus" "Mary" "Paty"
## [42,] "Adriana" "Alonso" "Angel" "Jesus" "Olga" "Paty"
## [43,] "Adriana" "Alonso" "Angel" "Juan" "Mary" "Paty"
## [44,] "Adriana" "Alonso" "Angel" "Juan" "Olga" "Paty"
## [45,] "Adriana" "Alonso" "Angel" "Mary" "Olga" "Paty"
## [46,] "Adriana" "Alonso" "Augustus" "Jesus" "Juan" "Paty"
## [47,] "Adriana" "Alonso" "Augustus" "Jesus" "Mary" "Paty"
## [48,] "Adriana" "Alonso" "Augustus" "Jesus" "Olga" "Paty"
## [49,] "Adriana" "Alonso" "Augustus" "Juan" "Mary" "Paty"
## [50,] "Adriana" "Alonso" "Augustus" "Juan" "Olga" "Paty"
## [51,] "Adriana" "Alonso" "Augustus" "Mary" "Olga" "Paty"
## [52,] "Adriana" "Alonso" "Jesus" "Juan" "Mary" "Paty"
## [53,] "Adriana" "Alonso" "Jesus" "Juan" "Olga" "Paty"
## [54,] "Adriana" "Alonso" "Jesus" "Mary" "Olga" "Paty"
## [55,] "Adriana" "Alonso" "Juan" "Mary" "Olga" "Paty"
## [56,] "Adriana" "Angel" "Augustus" "Jesus" "Juan" "Paty"
## [57,] "Adriana" "Angel" "Augustus" "Jesus" "Mary" "Paty"
## [58,] "Adriana" "Angel" "Augustus" "Jesus" "Olga" "Paty"
## [59,] "Adriana" "Angel" "Augustus" "Juan" "Mary" "Paty"
## [60,] "Adriana" "Angel" "Augustus" "Juan" "Olga" "Paty"
## [61,] "Adriana" "Angel" "Augustus" "Mary" "Olga" "Paty"
## [62,] "Adriana" "Angel" "Jesus" "Juan" "Mary" "Paty"
## [63,] "Adriana" "Angel" "Jesus" "Juan" "Olga" "Paty"
## [64,] "Adriana" "Angel" "Jesus" "Mary" "Olga" "Paty"
## [65,] "Adriana" "Angel" "Juan" "Mary" "Olga" "Paty"
## [66,] "Adriana" "Augustus" "Jesus" "Juan" "Mary" "Paty"
## [67,] "Adriana" "Augustus" "Jesus" "Juan" "Olga" "Paty"
## [68,] "Adriana" "Augustus" "Jesus" "Mary" "Olga" "Paty"
## [69,] "Adriana" "Augustus" "Juan" "Mary" "Olga" "Paty"
## [70,] "Adriana" "Jesus" "Juan" "Mary" "Olga" "Paty"
## [71,] "Ahri" "Alonso" "Angel" "Augustus" "Jesus" "Paty"
## [72,] "Ahri" "Alonso" "Angel" "Augustus" "Juan" "Paty"
## [73,] "Ahri" "Alonso" "Angel" "Augustus" "Mary" "Paty"
## [74,] "Ahri" "Alonso" "Angel" "Augustus" "Olga" "Paty"
## [75,] "Ahri" "Alonso" "Angel" "Jesus" "Juan" "Paty"
## [76,] "Ahri" "Alonso" "Angel" "Jesus" "Mary" "Paty"
## [77,] "Ahri" "Alonso" "Angel" "Jesus" "Olga" "Paty"
## [78,] "Ahri" "Alonso" "Angel" "Juan" "Mary" "Paty"
## [79,] "Ahri" "Alonso" "Angel" "Juan" "Olga" "Paty"
## [80,] "Ahri" "Alonso" "Angel" "Mary" "Olga" "Paty"
## [81,] "Ahri" "Alonso" "Augustus" "Jesus" "Juan" "Paty"
## [82,] "Ahri" "Alonso" "Augustus" "Jesus" "Mary" "Paty"
## [83,] "Ahri" "Alonso" "Augustus" "Jesus" "Olga" "Paty"
## [84,] "Ahri" "Alonso" "Augustus" "Juan" "Mary" "Paty"
## [85,] "Ahri" "Alonso" "Augustus" "Juan" "Olga" "Paty"
## [86,] "Ahri" "Alonso" "Augustus" "Mary" "Olga" "Paty"
## [87,] "Ahri" "Alonso" "Jesus" "Juan" "Mary" "Paty"
## [88,] "Ahri" "Alonso" "Jesus" "Juan" "Olga" "Paty"
## [89,] "Ahri" "Alonso" "Jesus" "Mary" "Olga" "Paty"
## [90,] "Ahri" "Alonso" "Juan" "Mary" "Olga" "Paty"
## [91,] "Ahri" "Angel" "Augustus" "Jesus" "Juan" "Paty"
## [92,] "Ahri" "Angel" "Augustus" "Jesus" "Mary" "Paty"
## [93,] "Ahri" "Angel" "Augustus" "Jesus" "Olga" "Paty"
## [94,] "Ahri" "Angel" "Augustus" "Juan" "Mary" "Paty"
## [95,] "Ahri" "Angel" "Augustus" "Juan" "Olga" "Paty"
## [96,] "Ahri" "Angel" "Augustus" "Mary" "Olga" "Paty"
## [97,] "Ahri" "Angel" "Jesus" "Juan" "Mary" "Paty"
## [98,] "Ahri" "Angel" "Jesus" "Juan" "Olga" "Paty"
## [99,] "Ahri" "Angel" "Jesus" "Mary" "Olga" "Paty"
## [100,] "Ahri" "Angel" "Juan" "Mary" "Olga" "Paty"
## [101,] "Ahri" "Augustus" "Jesus" "Juan" "Mary" "Paty"
## [102,] "Ahri" "Augustus" "Jesus" "Juan" "Olga" "Paty"
## [103,] "Ahri" "Augustus" "Jesus" "Mary" "Olga" "Paty"
## [104,] "Ahri" "Augustus" "Juan" "Mary" "Olga" "Paty"
## [105,] "Ahri" "Jesus" "Juan" "Mary" "Olga" "Paty"
## [106,] "Alonso" "Angel" "Augustus" "Jesus" "Juan" "Paty"
## [107,] "Alonso" "Angel" "Augustus" "Jesus" "Mary" "Paty"
## [108,] "Alonso" "Angel" "Augustus" "Jesus" "Olga" "Paty"
## [109,] "Alonso" "Angel" "Augustus" "Juan" "Mary" "Paty"
## [110,] "Alonso" "Angel" "Augustus" "Juan" "Olga" "Paty"
## [111,] "Alonso" "Angel" "Augustus" "Mary" "Olga" "Paty"
## [112,] "Alonso" "Angel" "Jesus" "Juan" "Mary" "Paty"
## [113,] "Alonso" "Angel" "Jesus" "Juan" "Olga" "Paty"
## [114,] "Alonso" "Angel" "Jesus" "Mary" "Olga" "Paty"
## [115,] "Alonso" "Angel" "Juan" "Mary" "Olga" "Paty"
## [116,] "Alonso" "Augustus" "Jesus" "Juan" "Mary" "Paty"
## [117,] "Alonso" "Augustus" "Jesus" "Juan" "Olga" "Paty"
## [118,] "Alonso" "Augustus" "Jesus" "Mary" "Olga" "Paty"
## [119,] "Alonso" "Augustus" "Juan" "Mary" "Olga" "Paty"
## [120,] "Alonso" "Jesus" "Juan" "Mary" "Olga" "Paty"
## [121,] "Angel" "Augustus" "Jesus" "Juan" "Mary" "Paty"
## [122,] "Angel" "Augustus" "Jesus" "Juan" "Olga" "Paty"
## [123,] "Angel" "Augustus" "Jesus" "Mary" "Olga" "Paty"
## [124,] "Angel" "Augustus" "Juan" "Mary" "Olga" "Paty"
## [125,] "Angel" "Jesus" "Juan" "Mary" "Olga" "Paty"
## [126,] "Augustus" "Jesus" "Juan" "Mary" "Olga" "Paty"
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,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Olga"
## [2,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Olga"
## [3,] "Adriana" "Ahri" "Alonso" "Angel" "Juan" "Olga"
## [4,] "Adriana" "Ahri" "Alonso" "Angel" "Mary" "Olga"
## [5,] "Adriana" "Ahri" "Alonso" "Angel" "Olga" "Paty"
## [6,] "Adriana" "Ahri" "Alonso" "Augustus" "Jesus" "Olga"
## [7,] "Adriana" "Ahri" "Alonso" "Augustus" "Juan" "Olga"
## [8,] "Adriana" "Ahri" "Alonso" "Augustus" "Mary" "Olga"
## [9,] "Adriana" "Ahri" "Alonso" "Augustus" "Olga" "Paty"
## [10,] "Adriana" "Ahri" "Alonso" "Jesus" "Juan" "Olga"
## [11,] "Adriana" "Ahri" "Alonso" "Jesus" "Mary" "Olga"
## [12,] "Adriana" "Ahri" "Alonso" "Jesus" "Olga" "Paty"
## [13,] "Adriana" "Ahri" "Alonso" "Juan" "Mary" "Olga"
## [14,] "Adriana" "Ahri" "Alonso" "Juan" "Olga" "Paty"
## [15,] "Adriana" "Ahri" "Alonso" "Mary" "Olga" "Paty"
## [16,] "Adriana" "Ahri" "Angel" "Augustus" "Jesus" "Olga"
## [17,] "Adriana" "Ahri" "Angel" "Augustus" "Juan" "Olga"
## [18,] "Adriana" "Ahri" "Angel" "Augustus" "Mary" "Olga"
## [19,] "Adriana" "Ahri" "Angel" "Augustus" "Olga" "Paty"
## [20,] "Adriana" "Ahri" "Angel" "Jesus" "Juan" "Olga"
## [21,] "Adriana" "Ahri" "Angel" "Jesus" "Mary" "Olga"
## [22,] "Adriana" "Ahri" "Angel" "Jesus" "Olga" "Paty"
## [23,] "Adriana" "Ahri" "Angel" "Juan" "Mary" "Olga"
## [24,] "Adriana" "Ahri" "Angel" "Juan" "Olga" "Paty"
## [25,] "Adriana" "Ahri" "Angel" "Mary" "Olga" "Paty"
## [26,] "Adriana" "Ahri" "Augustus" "Jesus" "Juan" "Olga"
## [27,] "Adriana" "Ahri" "Augustus" "Jesus" "Mary" "Olga"
## [28,] "Adriana" "Ahri" "Augustus" "Jesus" "Olga" "Paty"
## [29,] "Adriana" "Ahri" "Augustus" "Juan" "Mary" "Olga"
## [30,] "Adriana" "Ahri" "Augustus" "Juan" "Olga" "Paty"
## [31,] "Adriana" "Ahri" "Augustus" "Mary" "Olga" "Paty"
## [32,] "Adriana" "Ahri" "Jesus" "Juan" "Mary" "Olga"
## [33,] "Adriana" "Ahri" "Jesus" "Juan" "Olga" "Paty"
## [34,] "Adriana" "Ahri" "Jesus" "Mary" "Olga" "Paty"
## [35,] "Adriana" "Ahri" "Juan" "Mary" "Olga" "Paty"
## [36,] "Adriana" "Alonso" "Angel" "Augustus" "Jesus" "Olga"
## [37,] "Adriana" "Alonso" "Angel" "Augustus" "Juan" "Olga"
## [38,] "Adriana" "Alonso" "Angel" "Augustus" "Mary" "Olga"
## [39,] "Adriana" "Alonso" "Angel" "Augustus" "Olga" "Paty"
## [40,] "Adriana" "Alonso" "Angel" "Jesus" "Juan" "Olga"
## [41,] "Adriana" "Alonso" "Angel" "Jesus" "Mary" "Olga"
## [42,] "Adriana" "Alonso" "Angel" "Jesus" "Olga" "Paty"
## [43,] "Adriana" "Alonso" "Angel" "Juan" "Mary" "Olga"
## [44,] "Adriana" "Alonso" "Angel" "Juan" "Olga" "Paty"
## [45,] "Adriana" "Alonso" "Angel" "Mary" "Olga" "Paty"
## [46,] "Adriana" "Alonso" "Augustus" "Jesus" "Juan" "Olga"
## [47,] "Adriana" "Alonso" "Augustus" "Jesus" "Mary" "Olga"
## [48,] "Adriana" "Alonso" "Augustus" "Jesus" "Olga" "Paty"
## [49,] "Adriana" "Alonso" "Augustus" "Juan" "Mary" "Olga"
## [50,] "Adriana" "Alonso" "Augustus" "Juan" "Olga" "Paty"
## [51,] "Adriana" "Alonso" "Augustus" "Mary" "Olga" "Paty"
## [52,] "Adriana" "Alonso" "Jesus" "Juan" "Mary" "Olga"
## [53,] "Adriana" "Alonso" "Jesus" "Juan" "Olga" "Paty"
## [54,] "Adriana" "Alonso" "Jesus" "Mary" "Olga" "Paty"
## [55,] "Adriana" "Alonso" "Juan" "Mary" "Olga" "Paty"
## [56,] "Adriana" "Angel" "Augustus" "Jesus" "Juan" "Olga"
## [57,] "Adriana" "Angel" "Augustus" "Jesus" "Mary" "Olga"
## [58,] "Adriana" "Angel" "Augustus" "Jesus" "Olga" "Paty"
## [59,] "Adriana" "Angel" "Augustus" "Juan" "Mary" "Olga"
## [60,] "Adriana" "Angel" "Augustus" "Juan" "Olga" "Paty"
## [61,] "Adriana" "Angel" "Augustus" "Mary" "Olga" "Paty"
## [62,] "Adriana" "Angel" "Jesus" "Juan" "Mary" "Olga"
## [63,] "Adriana" "Angel" "Jesus" "Juan" "Olga" "Paty"
## [64,] "Adriana" "Angel" "Jesus" "Mary" "Olga" "Paty"
## [65,] "Adriana" "Angel" "Juan" "Mary" "Olga" "Paty"
## [66,] "Adriana" "Augustus" "Jesus" "Juan" "Mary" "Olga"
## [67,] "Adriana" "Augustus" "Jesus" "Juan" "Olga" "Paty"
## [68,] "Adriana" "Augustus" "Jesus" "Mary" "Olga" "Paty"
## [69,] "Adriana" "Augustus" "Juan" "Mary" "Olga" "Paty"
## [70,] "Adriana" "Jesus" "Juan" "Mary" "Olga" "Paty"
## [71,] "Ahri" "Alonso" "Angel" "Augustus" "Jesus" "Olga"
## [72,] "Ahri" "Alonso" "Angel" "Augustus" "Juan" "Olga"
## [73,] "Ahri" "Alonso" "Angel" "Augustus" "Mary" "Olga"
## [74,] "Ahri" "Alonso" "Angel" "Augustus" "Olga" "Paty"
## [75,] "Ahri" "Alonso" "Angel" "Jesus" "Juan" "Olga"
## [76,] "Ahri" "Alonso" "Angel" "Jesus" "Mary" "Olga"
## [77,] "Ahri" "Alonso" "Angel" "Jesus" "Olga" "Paty"
## [78,] "Ahri" "Alonso" "Angel" "Juan" "Mary" "Olga"
## [79,] "Ahri" "Alonso" "Angel" "Juan" "Olga" "Paty"
## [80,] "Ahri" "Alonso" "Angel" "Mary" "Olga" "Paty"
## [81,] "Ahri" "Alonso" "Augustus" "Jesus" "Juan" "Olga"
## [82,] "Ahri" "Alonso" "Augustus" "Jesus" "Mary" "Olga"
## [83,] "Ahri" "Alonso" "Augustus" "Jesus" "Olga" "Paty"
## [84,] "Ahri" "Alonso" "Augustus" "Juan" "Mary" "Olga"
## [85,] "Ahri" "Alonso" "Augustus" "Juan" "Olga" "Paty"
## [86,] "Ahri" "Alonso" "Augustus" "Mary" "Olga" "Paty"
## [87,] "Ahri" "Alonso" "Jesus" "Juan" "Mary" "Olga"
## [88,] "Ahri" "Alonso" "Jesus" "Juan" "Olga" "Paty"
## [89,] "Ahri" "Alonso" "Jesus" "Mary" "Olga" "Paty"
## [90,] "Ahri" "Alonso" "Juan" "Mary" "Olga" "Paty"
## [91,] "Ahri" "Angel" "Augustus" "Jesus" "Juan" "Olga"
## [92,] "Ahri" "Angel" "Augustus" "Jesus" "Mary" "Olga"
## [93,] "Ahri" "Angel" "Augustus" "Jesus" "Olga" "Paty"
## [94,] "Ahri" "Angel" "Augustus" "Juan" "Mary" "Olga"
## [95,] "Ahri" "Angel" "Augustus" "Juan" "Olga" "Paty"
## [96,] "Ahri" "Angel" "Augustus" "Mary" "Olga" "Paty"
## [97,] "Ahri" "Angel" "Jesus" "Juan" "Mary" "Olga"
## [98,] "Ahri" "Angel" "Jesus" "Juan" "Olga" "Paty"
## [99,] "Ahri" "Angel" "Jesus" "Mary" "Olga" "Paty"
## [100,] "Ahri" "Angel" "Juan" "Mary" "Olga" "Paty"
## [101,] "Ahri" "Augustus" "Jesus" "Juan" "Mary" "Olga"
## [102,] "Ahri" "Augustus" "Jesus" "Juan" "Olga" "Paty"
## [103,] "Ahri" "Augustus" "Jesus" "Mary" "Olga" "Paty"
## [104,] "Ahri" "Augustus" "Juan" "Mary" "Olga" "Paty"
## [105,] "Ahri" "Jesus" "Juan" "Mary" "Olga" "Paty"
## [106,] "Alonso" "Angel" "Augustus" "Jesus" "Juan" "Olga"
## [107,] "Alonso" "Angel" "Augustus" "Jesus" "Mary" "Olga"
## [108,] "Alonso" "Angel" "Augustus" "Jesus" "Olga" "Paty"
## [109,] "Alonso" "Angel" "Augustus" "Juan" "Mary" "Olga"
## [110,] "Alonso" "Angel" "Augustus" "Juan" "Olga" "Paty"
## [111,] "Alonso" "Angel" "Augustus" "Mary" "Olga" "Paty"
## [112,] "Alonso" "Angel" "Jesus" "Juan" "Mary" "Olga"
## [113,] "Alonso" "Angel" "Jesus" "Juan" "Olga" "Paty"
## [114,] "Alonso" "Angel" "Jesus" "Mary" "Olga" "Paty"
## [115,] "Alonso" "Angel" "Juan" "Mary" "Olga" "Paty"
## [116,] "Alonso" "Augustus" "Jesus" "Juan" "Mary" "Olga"
## [117,] "Alonso" "Augustus" "Jesus" "Juan" "Olga" "Paty"
## [118,] "Alonso" "Augustus" "Jesus" "Mary" "Olga" "Paty"
## [119,] "Alonso" "Augustus" "Juan" "Mary" "Olga" "Paty"
## [120,] "Alonso" "Jesus" "Juan" "Mary" "Olga" "Paty"
## [121,] "Angel" "Augustus" "Jesus" "Juan" "Mary" "Olga"
## [122,] "Angel" "Augustus" "Jesus" "Juan" "Olga" "Paty"
## [123,] "Angel" "Augustus" "Jesus" "Mary" "Olga" "Paty"
## [124,] "Angel" "Augustus" "Juan" "Mary" "Olga" "Paty"
## [125,] "Angel" "Jesus" "Juan" "Mary" "Olga" "Paty"
## [126,] "Augustus" "Jesus" "Juan" "Mary" "Olga" "Paty"
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,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Olga"
## [2,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Olga"
## [3,] "Adriana" "Ahri" "Alonso" "Angel" "Juan" "Olga"
## [4,] "Adriana" "Ahri" "Alonso" "Angel" "Mary" "Olga"
## [5,] "Adriana" "Ahri" "Alonso" "Angel" "Olga" "Paty"
## [6,] "Adriana" "Ahri" "Alonso" "Augustus" "Jesus" "Olga"
## [7,] "Adriana" "Ahri" "Alonso" "Augustus" "Juan" "Olga"
## [8,] "Adriana" "Ahri" "Alonso" "Augustus" "Mary" "Olga"
## [9,] "Adriana" "Ahri" "Alonso" "Augustus" "Olga" "Paty"
## [10,] "Adriana" "Ahri" "Alonso" "Jesus" "Juan" "Olga"
## [11,] "Adriana" "Ahri" "Alonso" "Jesus" "Mary" "Olga"
## [12,] "Adriana" "Ahri" "Alonso" "Jesus" "Olga" "Paty"
## [13,] "Adriana" "Ahri" "Alonso" "Juan" "Mary" "Olga"
## [14,] "Adriana" "Ahri" "Alonso" "Juan" "Olga" "Paty"
## [15,] "Adriana" "Ahri" "Alonso" "Mary" "Olga" "Paty"
## [16,] "Adriana" "Ahri" "Angel" "Augustus" "Jesus" "Olga"
## [17,] "Adriana" "Ahri" "Angel" "Augustus" "Juan" "Olga"
## [18,] "Adriana" "Ahri" "Angel" "Augustus" "Mary" "Olga"
## [19,] "Adriana" "Ahri" "Angel" "Augustus" "Olga" "Paty"
## [20,] "Adriana" "Ahri" "Angel" "Jesus" "Juan" "Olga"
## [21,] "Adriana" "Ahri" "Angel" "Jesus" "Mary" "Olga"
## [22,] "Adriana" "Ahri" "Angel" "Jesus" "Olga" "Paty"
## [23,] "Adriana" "Ahri" "Angel" "Juan" "Mary" "Olga"
## [24,] "Adriana" "Ahri" "Angel" "Juan" "Olga" "Paty"
## [25,] "Adriana" "Ahri" "Angel" "Mary" "Olga" "Paty"
## [26,] "Adriana" "Ahri" "Augustus" "Jesus" "Juan" "Olga"
## [27,] "Adriana" "Ahri" "Augustus" "Jesus" "Mary" "Olga"
## [28,] "Adriana" "Ahri" "Augustus" "Jesus" "Olga" "Paty"
## [29,] "Adriana" "Ahri" "Augustus" "Juan" "Mary" "Olga"
## [30,] "Adriana" "Ahri" "Augustus" "Juan" "Olga" "Paty"
## [31,] "Adriana" "Ahri" "Augustus" "Mary" "Olga" "Paty"
## [32,] "Adriana" "Ahri" "Jesus" "Juan" "Mary" "Olga"
## [33,] "Adriana" "Ahri" "Jesus" "Juan" "Olga" "Paty"
## [34,] "Adriana" "Ahri" "Jesus" "Mary" "Olga" "Paty"
## [35,] "Adriana" "Ahri" "Juan" "Mary" "Olga" "Paty"
## [36,] "Adriana" "Alonso" "Angel" "Augustus" "Jesus" "Olga"
## [37,] "Adriana" "Alonso" "Angel" "Augustus" "Juan" "Olga"
## [38,] "Adriana" "Alonso" "Angel" "Augustus" "Mary" "Olga"
## [39,] "Adriana" "Alonso" "Angel" "Augustus" "Olga" "Paty"
## [40,] "Adriana" "Alonso" "Angel" "Jesus" "Juan" "Olga"
## [41,] "Adriana" "Alonso" "Angel" "Jesus" "Mary" "Olga"
## [42,] "Adriana" "Alonso" "Angel" "Jesus" "Olga" "Paty"
## [43,] "Adriana" "Alonso" "Angel" "Juan" "Mary" "Olga"
## [44,] "Adriana" "Alonso" "Angel" "Juan" "Olga" "Paty"
## [45,] "Adriana" "Alonso" "Angel" "Mary" "Olga" "Paty"
## [46,] "Adriana" "Alonso" "Augustus" "Jesus" "Juan" "Olga"
## [47,] "Adriana" "Alonso" "Augustus" "Jesus" "Mary" "Olga"
## [48,] "Adriana" "Alonso" "Augustus" "Jesus" "Olga" "Paty"
## [49,] "Adriana" "Alonso" "Augustus" "Juan" "Mary" "Olga"
## [50,] "Adriana" "Alonso" "Augustus" "Juan" "Olga" "Paty"
## [51,] "Adriana" "Alonso" "Augustus" "Mary" "Olga" "Paty"
## [52,] "Adriana" "Alonso" "Jesus" "Juan" "Mary" "Olga"
## [53,] "Adriana" "Alonso" "Jesus" "Juan" "Olga" "Paty"
## [54,] "Adriana" "Alonso" "Jesus" "Mary" "Olga" "Paty"
## [55,] "Adriana" "Alonso" "Juan" "Mary" "Olga" "Paty"
## [56,] "Adriana" "Angel" "Augustus" "Jesus" "Juan" "Olga"
## [57,] "Adriana" "Angel" "Augustus" "Jesus" "Mary" "Olga"
## [58,] "Adriana" "Angel" "Augustus" "Jesus" "Olga" "Paty"
## [59,] "Adriana" "Angel" "Augustus" "Juan" "Mary" "Olga"
## [60,] "Adriana" "Angel" "Augustus" "Juan" "Olga" "Paty"
## [61,] "Adriana" "Angel" "Augustus" "Mary" "Olga" "Paty"
## [62,] "Adriana" "Angel" "Jesus" "Juan" "Mary" "Olga"
## [63,] "Adriana" "Angel" "Jesus" "Juan" "Olga" "Paty"
## [64,] "Adriana" "Angel" "Jesus" "Mary" "Olga" "Paty"
## [65,] "Adriana" "Angel" "Juan" "Mary" "Olga" "Paty"
## [66,] "Adriana" "Augustus" "Jesus" "Juan" "Mary" "Olga"
## [67,] "Adriana" "Augustus" "Jesus" "Juan" "Olga" "Paty"
## [68,] "Adriana" "Augustus" "Jesus" "Mary" "Olga" "Paty"
## [69,] "Adriana" "Augustus" "Juan" "Mary" "Olga" "Paty"
## [70,] "Adriana" "Jesus" "Juan" "Mary" "Olga" "Paty"
## [71,] "Ahri" "Alonso" "Angel" "Augustus" "Jesus" "Olga"
## [72,] "Ahri" "Alonso" "Angel" "Augustus" "Juan" "Olga"
## [73,] "Ahri" "Alonso" "Angel" "Augustus" "Mary" "Olga"
## [74,] "Ahri" "Alonso" "Angel" "Augustus" "Olga" "Paty"
## [75,] "Ahri" "Alonso" "Angel" "Jesus" "Juan" "Olga"
## [76,] "Ahri" "Alonso" "Angel" "Jesus" "Mary" "Olga"
## [77,] "Ahri" "Alonso" "Angel" "Jesus" "Olga" "Paty"
## [78,] "Ahri" "Alonso" "Angel" "Juan" "Mary" "Olga"
## [79,] "Ahri" "Alonso" "Angel" "Juan" "Olga" "Paty"
## [80,] "Ahri" "Alonso" "Angel" "Mary" "Olga" "Paty"
## [81,] "Ahri" "Alonso" "Augustus" "Jesus" "Juan" "Olga"
## [82,] "Ahri" "Alonso" "Augustus" "Jesus" "Mary" "Olga"
## [83,] "Ahri" "Alonso" "Augustus" "Jesus" "Olga" "Paty"
## [84,] "Ahri" "Alonso" "Augustus" "Juan" "Mary" "Olga"
## [85,] "Ahri" "Alonso" "Augustus" "Juan" "Olga" "Paty"
## [86,] "Ahri" "Alonso" "Augustus" "Mary" "Olga" "Paty"
## [87,] "Ahri" "Alonso" "Jesus" "Juan" "Mary" "Olga"
## [88,] "Ahri" "Alonso" "Jesus" "Juan" "Olga" "Paty"
## [89,] "Ahri" "Alonso" "Jesus" "Mary" "Olga" "Paty"
## [90,] "Ahri" "Alonso" "Juan" "Mary" "Olga" "Paty"
## [91,] "Ahri" "Angel" "Augustus" "Jesus" "Juan" "Olga"
## [92,] "Ahri" "Angel" "Augustus" "Jesus" "Mary" "Olga"
## [93,] "Ahri" "Angel" "Augustus" "Jesus" "Olga" "Paty"
## [94,] "Ahri" "Angel" "Augustus" "Juan" "Mary" "Olga"
## [95,] "Ahri" "Angel" "Augustus" "Juan" "Olga" "Paty"
## [96,] "Ahri" "Angel" "Augustus" "Mary" "Olga" "Paty"
## [97,] "Ahri" "Angel" "Jesus" "Juan" "Mary" "Olga"
## [98,] "Ahri" "Angel" "Jesus" "Juan" "Olga" "Paty"
## [99,] "Ahri" "Angel" "Jesus" "Mary" "Olga" "Paty"
## [100,] "Ahri" "Angel" "Juan" "Mary" "Olga" "Paty"
## [101,] "Ahri" "Augustus" "Jesus" "Juan" "Mary" "Olga"
## [102,] "Ahri" "Augustus" "Jesus" "Juan" "Olga" "Paty"
## [103,] "Ahri" "Augustus" "Jesus" "Mary" "Olga" "Paty"
## [104,] "Ahri" "Augustus" "Juan" "Mary" "Olga" "Paty"
## [105,] "Ahri" "Jesus" "Juan" "Mary" "Olga" "Paty"
## [106,] "Alonso" "Angel" "Augustus" "Jesus" "Juan" "Olga"
## [107,] "Alonso" "Angel" "Augustus" "Jesus" "Mary" "Olga"
## [108,] "Alonso" "Angel" "Augustus" "Jesus" "Olga" "Paty"
## [109,] "Alonso" "Angel" "Augustus" "Juan" "Mary" "Olga"
## [110,] "Alonso" "Angel" "Augustus" "Juan" "Olga" "Paty"
## [111,] "Alonso" "Angel" "Augustus" "Mary" "Olga" "Paty"
## [112,] "Alonso" "Angel" "Jesus" "Juan" "Mary" "Olga"
## [113,] "Alonso" "Angel" "Jesus" "Juan" "Olga" "Paty"
## [114,] "Alonso" "Angel" "Jesus" "Mary" "Olga" "Paty"
## [115,] "Alonso" "Angel" "Juan" "Mary" "Olga" "Paty"
## [116,] "Alonso" "Augustus" "Jesus" "Juan" "Mary" "Olga"
## [117,] "Alonso" "Augustus" "Jesus" "Juan" "Olga" "Paty"
## [118,] "Alonso" "Augustus" "Jesus" "Mary" "Olga" "Paty"
## [119,] "Alonso" "Augustus" "Juan" "Mary" "Olga" "Paty"
## [120,] "Alonso" "Jesus" "Juan" "Mary" "Olga" "Paty"
## [121,] "Angel" "Augustus" "Jesus" "Juan" "Mary" "Olga"
## [122,] "Angel" "Augustus" "Jesus" "Juan" "Olga" "Paty"
## [123,] "Angel" "Augustus" "Jesus" "Mary" "Olga" "Paty"
## [124,] "Angel" "Augustus" "Juan" "Mary" "Olga" "Paty"
## [125,] "Angel" "Jesus" "Juan" "Mary" "Olga" "Paty"
## [126,] "Augustus" "Jesus" "Juan" "Mary" "Olga" "Paty"
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,] "Adriana" "Ahri" "Alonso" "Mary" "Olga" "Paty"
## [2,] "Adriana" "Ahri" "Angel" "Mary" "Olga" "Paty"
## [3,] "Adriana" "Ahri" "Augustus" "Mary" "Olga" "Paty"
## [4,] "Adriana" "Ahri" "Jesus" "Mary" "Olga" "Paty"
## [5,] "Adriana" "Ahri" "Juan" "Mary" "Olga" "Paty"
## [6,] "Adriana" "Alonso" "Angel" "Mary" "Olga" "Paty"
## [7,] "Adriana" "Alonso" "Augustus" "Mary" "Olga" "Paty"
## [8,] "Adriana" "Alonso" "Jesus" "Mary" "Olga" "Paty"
## [9,] "Adriana" "Alonso" "Juan" "Mary" "Olga" "Paty"
## [10,] "Adriana" "Angel" "Augustus" "Mary" "Olga" "Paty"
## [11,] "Adriana" "Angel" "Jesus" "Mary" "Olga" "Paty"
## [12,] "Adriana" "Angel" "Juan" "Mary" "Olga" "Paty"
## [13,] "Adriana" "Augustus" "Jesus" "Mary" "Olga" "Paty"
## [14,] "Adriana" "Augustus" "Juan" "Mary" "Olga" "Paty"
## [15,] "Adriana" "Jesus" "Juan" "Mary" "Olga" "Paty"
head(permutaciones[which(permutaciones[,1] == 'Adriana'),])
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Jesus"
## [2,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Juan"
## [3,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Mary"
## [4,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Olga"
## [5,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Paty"
## [6,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Augustus"
tail(permutaciones[which(permutaciones[,1] == 'Adriana'),])
## [,1] [,2] [,3] [,4] [,5] [,6]
## [15115,] "Adriana" "Paty" "Olga" "Mary" "Jesus" "Juan"
## [15116,] "Adriana" "Paty" "Olga" "Mary" "Juan" "Ahri"
## [15117,] "Adriana" "Paty" "Olga" "Mary" "Juan" "Alonso"
## [15118,] "Adriana" "Paty" "Olga" "Mary" "Juan" "Angel"
## [15119,] "Adriana" "Paty" "Olga" "Mary" "Juan" "Augustus"
## [15120,] "Adriana" "Paty" "Olga" "Mary" "Juan" "Jesus"
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,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Jesus"
## [2,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Juan"
## [3,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Mary"
## [4,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Olga"
## [5,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Paty"
## [6,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Augustus"
tail(permutaciones[which(permutaciones[,1] == 'Adriana' | permutaciones[,2] == 'Adriana' | permutaciones[,3] == 'Adriana'),])
## [,1] [,2] [,3] [,4] [,5] [,6]
## [45355,] "Paty" "Olga" "Adriana" "Mary" "Jesus" "Juan"
## [45356,] "Paty" "Olga" "Adriana" "Mary" "Juan" "Ahri"
## [45357,] "Paty" "Olga" "Adriana" "Mary" "Juan" "Alonso"
## [45358,] "Paty" "Olga" "Adriana" "Mary" "Juan" "Angel"
## [45359,] "Paty" "Olga" "Adriana" "Mary" "Juan" "Augustus"
## [45360,] "Paty" "Olga" "Adriana" "Mary" "Juan" "Jesus"
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,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Paty"
## [2,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Paty"
## [3,] "Adriana" "Ahri" "Alonso" "Angel" "Juan" "Paty"
## [4,] "Adriana" "Ahri" "Alonso" "Angel" "Mary" "Paty"
## [5,] "Adriana" "Ahri" "Alonso" "Angel" "Olga" "Paty"
## [6,] "Adriana" "Ahri" "Alonso" "Angel" "Paty" "Augustus"
tail(permutaciones[which(permutaciones[,4] == 'Paty' | permutaciones[,5] == 'Paty' | permutaciones[,6] == 'Paty'),])
## [,1] [,2] [,3] [,4] [,5] [,6]
## [45355,] "Olga" "Mary" "Juan" "Paty" "Augustus" "Jesus"
## [45356,] "Olga" "Mary" "Juan" "Paty" "Jesus" "Adriana"
## [45357,] "Olga" "Mary" "Juan" "Paty" "Jesus" "Ahri"
## [45358,] "Olga" "Mary" "Juan" "Paty" "Jesus" "Alonso"
## [45359,] "Olga" "Mary" "Juan" "Paty" "Jesus" "Angel"
## [45360,] "Olga" "Mary" "Juan" "Paty" "Jesus" "Augustus"
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,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Olga"
## [2,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Olga"
## [3,] "Adriana" "Ahri" "Alonso" "Angel" "Juan" "Olga"
## [4,] "Adriana" "Ahri" "Alonso" "Angel" "Mary" "Olga"
## [5,] "Adriana" "Ahri" "Alonso" "Angel" "Olga" "Augustus"
## [6,] "Adriana" "Ahri" "Alonso" "Angel" "Olga" "Jesus"
tail(permutaciones[which(permutaciones[,4] == 'Olga' | permutaciones[,5] == 'Olga' | permutaciones[,6] == 'Olga'),])
## [,1] [,2] [,3] [,4] [,5] [,6]
## [45355,] "Paty" "Mary" "Juan" "Olga" "Augustus" "Jesus"
## [45356,] "Paty" "Mary" "Juan" "Olga" "Jesus" "Adriana"
## [45357,] "Paty" "Mary" "Juan" "Olga" "Jesus" "Ahri"
## [45358,] "Paty" "Mary" "Juan" "Olga" "Jesus" "Alonso"
## [45359,] "Paty" "Mary" "Juan" "Olga" "Jesus" "Angel"
## [45360,] "Paty" "Mary" "Juan" "Olga" "Jesus" "Augustus"
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,] "Adriana" "Ahri" "Alonso" "Angel" "Augustus" "Olga"
## [2,] "Adriana" "Ahri" "Alonso" "Angel" "Jesus" "Olga"
## [3,] "Adriana" "Ahri" "Alonso" "Angel" "Juan" "Olga"
## [4,] "Adriana" "Ahri" "Alonso" "Angel" "Mary" "Olga"
## [5,] "Adriana" "Ahri" "Alonso" "Angel" "Olga" "Augustus"
## [6,] "Adriana" "Ahri" "Alonso" "Angel" "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" "Juan" "Augustus" "Jesus"
## [90716,] "Paty" "Olga" "Mary" "Juan" "Jesus" "Adriana"
## [90717,] "Paty" "Olga" "Mary" "Juan" "Jesus" "Ahri"
## [90718,] "Paty" "Olga" "Mary" "Juan" "Jesus" "Alonso"
## [90719,] "Paty" "Olga" "Mary" "Juan" "Jesus" "Angel"
## [90720,] "Paty" "Olga" "Mary" "Juan" "Jesus" "Augustus"
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,] "Adriana" "Ahri" "Alonso" "Mary" "Olga" "Paty"
## [2,] "Adriana" "Ahri" "Alonso" "Mary" "Paty" "Olga"
## [3,] "Adriana" "Ahri" "Alonso" "Olga" "Mary" "Paty"
## [4,] "Adriana" "Ahri" "Alonso" "Olga" "Paty" "Mary"
## [5,] "Adriana" "Ahri" "Alonso" "Paty" "Mary" "Olga"
## [6,] "Adriana" "Ahri" "Alonso" "Paty" "Olga" "Mary"
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?.
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" "Juan" "Mary" "Adriana" "Jesus"
## [8996,] "Paty" "Olga" "Juan" "Mary" "Ahri" "Adriana"
## [8997,] "Paty" "Olga" "Juan" "Mary" "Alonso" "Adriana"
## [8998,] "Paty" "Olga" "Juan" "Mary" "Angel" "Adriana"
## [8999,] "Paty" "Olga" "Juan" "Mary" "Augustus" "Adriana"
## [9000,] "Paty" "Olga" "Juan" "Mary" "Jesus" "Adriana"
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,] "Adriana" "Mary" "Olga" "Paty" "Ahri" "Alonso"
## [2,] "Adriana" "Mary" "Olga" "Paty" "Ahri" "Angel"
## [3,] "Adriana" "Mary" "Olga" "Paty" "Ahri" "Augustus"
## [4,] "Adriana" "Mary" "Olga" "Paty" "Ahri" "Jesus"
## [5,] "Adriana" "Mary" "Olga" "Paty" "Ahri" "Juan"
## [6,] "Adriana" "Mary" "Olga" "Paty" "Alonso" "Ahri"
## [7,] "Adriana" "Mary" "Olga" "Paty" "Alonso" "Angel"
## [8,] "Adriana" "Mary" "Olga" "Paty" "Alonso" "Augustus"
## [9,] "Adriana" "Mary" "Olga" "Paty" "Alonso" "Jesus"
## [10,] "Adriana" "Mary" "Olga" "Paty" "Alonso" "Juan"
## [11,] "Adriana" "Mary" "Olga" "Paty" "Angel" "Ahri"
## [12,] "Adriana" "Mary" "Olga" "Paty" "Angel" "Alonso"
## [13,] "Adriana" "Mary" "Olga" "Paty" "Angel" "Augustus"
## [14,] "Adriana" "Mary" "Olga" "Paty" "Angel" "Jesus"
## [15,] "Adriana" "Mary" "Olga" "Paty" "Angel" "Juan"
## [16,] "Adriana" "Mary" "Olga" "Paty" "Augustus" "Ahri"
## [17,] "Adriana" "Mary" "Olga" "Paty" "Augustus" "Alonso"
## [18,] "Adriana" "Mary" "Olga" "Paty" "Augustus" "Angel"
## [19,] "Adriana" "Mary" "Olga" "Paty" "Augustus" "Jesus"
## [20,] "Adriana" "Mary" "Olga" "Paty" "Augustus" "Juan"
## [21,] "Adriana" "Mary" "Olga" "Paty" "Jesus" "Ahri"
## [22,] "Adriana" "Mary" "Olga" "Paty" "Jesus" "Alonso"
## [23,] "Adriana" "Mary" "Olga" "Paty" "Jesus" "Angel"
## [24,] "Adriana" "Mary" "Olga" "Paty" "Jesus" "Augustus"
## [25,] "Adriana" "Mary" "Olga" "Paty" "Jesus" "Juan"
## [26,] "Adriana" "Mary" "Olga" "Paty" "Juan" "Ahri"
## [27,] "Adriana" "Mary" "Olga" "Paty" "Juan" "Alonso"
## [28,] "Adriana" "Mary" "Olga" "Paty" "Juan" "Angel"
## [29,] "Adriana" "Mary" "Olga" "Paty" "Juan" "Augustus"
## [30,] "Adriana" "Mary" "Olga" "Paty" "Juan" "Jesus"
## [31,] "Ahri" "Adriana" "Mary" "Olga" "Paty" "Alonso"
## [32,] "Ahri" "Adriana" "Mary" "Olga" "Paty" "Angel"
## [33,] "Ahri" "Adriana" "Mary" "Olga" "Paty" "Augustus"
## [34,] "Ahri" "Adriana" "Mary" "Olga" "Paty" "Jesus"
## [35,] "Ahri" "Adriana" "Mary" "Olga" "Paty" "Juan"
## [36,] "Ahri" "Alonso" "Adriana" "Mary" "Olga" "Paty"
## [37,] "Ahri" "Angel" "Adriana" "Mary" "Olga" "Paty"
## [38,] "Ahri" "Augustus" "Adriana" "Mary" "Olga" "Paty"
## [39,] "Ahri" "Jesus" "Adriana" "Mary" "Olga" "Paty"
## [40,] "Ahri" "Juan" "Adriana" "Mary" "Olga" "Paty"
## [41,] "Alonso" "Adriana" "Mary" "Olga" "Paty" "Ahri"
## [42,] "Alonso" "Adriana" "Mary" "Olga" "Paty" "Angel"
## [43,] "Alonso" "Adriana" "Mary" "Olga" "Paty" "Augustus"
## [44,] "Alonso" "Adriana" "Mary" "Olga" "Paty" "Jesus"
## [45,] "Alonso" "Adriana" "Mary" "Olga" "Paty" "Juan"
## [46,] "Alonso" "Ahri" "Adriana" "Mary" "Olga" "Paty"
## [47,] "Alonso" "Angel" "Adriana" "Mary" "Olga" "Paty"
## [48,] "Alonso" "Augustus" "Adriana" "Mary" "Olga" "Paty"
## [49,] "Alonso" "Jesus" "Adriana" "Mary" "Olga" "Paty"
## [50,] "Alonso" "Juan" "Adriana" "Mary" "Olga" "Paty"
## [51,] "Angel" "Adriana" "Mary" "Olga" "Paty" "Ahri"
## [52,] "Angel" "Adriana" "Mary" "Olga" "Paty" "Alonso"
## [53,] "Angel" "Adriana" "Mary" "Olga" "Paty" "Augustus"
## [54,] "Angel" "Adriana" "Mary" "Olga" "Paty" "Jesus"
## [55,] "Angel" "Adriana" "Mary" "Olga" "Paty" "Juan"
## [56,] "Angel" "Ahri" "Adriana" "Mary" "Olga" "Paty"
## [57,] "Angel" "Alonso" "Adriana" "Mary" "Olga" "Paty"
## [58,] "Angel" "Augustus" "Adriana" "Mary" "Olga" "Paty"
## [59,] "Angel" "Jesus" "Adriana" "Mary" "Olga" "Paty"
## [60,] "Angel" "Juan" "Adriana" "Mary" "Olga" "Paty"
## [61,] "Augustus" "Adriana" "Mary" "Olga" "Paty" "Ahri"
## [62,] "Augustus" "Adriana" "Mary" "Olga" "Paty" "Alonso"
## [63,] "Augustus" "Adriana" "Mary" "Olga" "Paty" "Angel"
## [64,] "Augustus" "Adriana" "Mary" "Olga" "Paty" "Jesus"
## [65,] "Augustus" "Adriana" "Mary" "Olga" "Paty" "Juan"
## [66,] "Augustus" "Ahri" "Adriana" "Mary" "Olga" "Paty"
## [67,] "Augustus" "Alonso" "Adriana" "Mary" "Olga" "Paty"
## [68,] "Augustus" "Angel" "Adriana" "Mary" "Olga" "Paty"
## [69,] "Augustus" "Jesus" "Adriana" "Mary" "Olga" "Paty"
## [70,] "Augustus" "Juan" "Adriana" "Mary" "Olga" "Paty"
## [71,] "Jesus" "Adriana" "Mary" "Olga" "Paty" "Ahri"
## [72,] "Jesus" "Adriana" "Mary" "Olga" "Paty" "Alonso"
## [73,] "Jesus" "Adriana" "Mary" "Olga" "Paty" "Angel"
## [74,] "Jesus" "Adriana" "Mary" "Olga" "Paty" "Augustus"
## [75,] "Jesus" "Adriana" "Mary" "Olga" "Paty" "Juan"
## [76,] "Jesus" "Ahri" "Adriana" "Mary" "Olga" "Paty"
## [77,] "Jesus" "Alonso" "Adriana" "Mary" "Olga" "Paty"
## [78,] "Jesus" "Angel" "Adriana" "Mary" "Olga" "Paty"
## [79,] "Jesus" "Augustus" "Adriana" "Mary" "Olga" "Paty"
## [80,] "Jesus" "Juan" "Adriana" "Mary" "Olga" "Paty"
## [81,] "Juan" "Adriana" "Mary" "Olga" "Paty" "Ahri"
## [82,] "Juan" "Adriana" "Mary" "Olga" "Paty" "Alonso"
## [83,] "Juan" "Adriana" "Mary" "Olga" "Paty" "Angel"
## [84,] "Juan" "Adriana" "Mary" "Olga" "Paty" "Augustus"
## [85,] "Juan" "Adriana" "Mary" "Olga" "Paty" "Jesus"
## [86,] "Juan" "Ahri" "Adriana" "Mary" "Olga" "Paty"
## [87,] "Juan" "Alonso" "Adriana" "Mary" "Olga" "Paty"
## [88,] "Juan" "Angel" "Adriana" "Mary" "Olga" "Paty"
## [89,] "Juan" "Augustus" "Adriana" "Mary" "Olga" "Paty"
## [90,] "Juan" "Jesus" "Adriana" "Mary" "Olga" "Paty"
Conclusion:
En este ejercicio pudimos practicar como hacer combinaciones y permutaciones con un conjunto de nombres, para distintos tamaños de conjuntos, ademas de analizar estos conjuntos con ciertas condiciones especificadas en la práctica, como por ejemplo cuantas combinaciones de 3 miembros se pueden hacer donde el nombre de la primer columna es “Adriana”.