library(gtools)
1 y 2.-Ingresar y ordenar datos
nombres <- c("Mario", "Jesabel", "Angel", "Jonhatan", "Augusto", "Daniel", "Paty", "Adriana", "Olga", "Mary")
nombres <- sort(nombres)
nombres
## [1] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Jonhatan"
## [7] "Mario" "Mary" "Olga" "Paty"
3.-Combinaciones en grupo de dos
N <- length(nombres)
n <- 2
combinaciones <- combinations(N, n, nombres)
head(combinaciones)
## [,1] [,2]
## [1,] "Adriana" "Angel"
## [2,] "Adriana" "Augusto"
## [3,] "Adriana" "Daniel"
## [4,] "Adriana" "Jesabel"
## [5,] "Adriana" "Jonhatan"
## [6,] "Adriana" "Mario"
nrow(combinaciones)
## [1] 45
factorial(N) / (factorial(n) * (factorial (N-n)))
## [1] 45
4.- Combinacion en grupo de cuatro
N <- length(nombres)
n <- 4
combinaciones <- combinations(N, n, nombres)
head(combinaciones)
## [,1] [,2] [,3] [,4]
## [1,] "Adriana" "Angel" "Augusto" "Daniel"
## [2,] "Adriana" "Angel" "Augusto" "Jesabel"
## [3,] "Adriana" "Angel" "Augusto" "Jonhatan"
## [4,] "Adriana" "Angel" "Augusto" "Mario"
## [5,] "Adriana" "Angel" "Augusto" "Mary"
## [6,] "Adriana" "Angel" "Augusto" "Olga"
nrow(combinaciones)
## [1] 210
factorial(N) / (factorial(n) * (factorial (N-n)))
## [1] 210
5.-Combinaciones en grupo de seis
N <- length(nombres)
n <- 6
combinaciones <- combinations(N, n, nombres)
head(combinaciones)
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Jonhatan"
## [2,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Mario"
## [3,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Mary"
## [4,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Olga"
## [5,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Paty"
## [6,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Mario"
nrow(combinaciones)
## [1] 210
factorial(N) / (factorial(n) * (factorial (N-n)))
## [1] 210
6.- Permutaciones en conjuto de dos
N <- length(nombres) # Cantidad de alumnos
n <- 2 # Grupos de 2
permutaciones <- permutations(N, n, nombres)
head(permutaciones)
## [,1] [,2]
## [1,] "Adriana" "Angel"
## [2,] "Adriana" "Augusto"
## [3,] "Adriana" "Daniel"
## [4,] "Adriana" "Jesabel"
## [5,] "Adriana" "Jonhatan"
## [6,] "Adriana" "Mario"
nrow(permutaciones)
## [1] 90
factorial(N) / (factorial (N-n))
## [1] 90
7.- Permutaciones en conjuto de cuatro
N <- length(nombres) # Cantidad de alumnos
n <- 4 # Grupos de 4
permutaciones <- permutations(N, n, nombres)
head(permutaciones)
## [,1] [,2] [,3] [,4]
## [1,] "Adriana" "Angel" "Augusto" "Daniel"
## [2,] "Adriana" "Angel" "Augusto" "Jesabel"
## [3,] "Adriana" "Angel" "Augusto" "Jonhatan"
## [4,] "Adriana" "Angel" "Augusto" "Mario"
## [5,] "Adriana" "Angel" "Augusto" "Mary"
## [6,] "Adriana" "Angel" "Augusto" "Olga"
nrow(permutaciones)
## [1] 5040
factorial(N) / (factorial (N-n))
## [1] 5040
8.- Permutaciones en conjuto de seis
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" "Angel" "Augusto" "Daniel" "Jesabel" "Jonhatan"
## [2,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Mario"
## [3,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Mary"
## [4,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Olga"
## [5,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Paty"
## [6,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Jesabel"
nrow(permutaciones)
## [1] 151200
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" "Angel" "Augusto" "Daniel" "Jesabel" "Jonhatan"
## [2,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Mario"
## [3,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Mary"
## [4,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Olga"
## [5,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Paty"
## [6,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Mario"
## [7,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Mary"
## [8,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Olga"
## [9,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Paty"
## [10,] "Adriana" "Angel" "Augusto" "Daniel" "Mario" "Mary"
## [11,] "Adriana" "Angel" "Augusto" "Daniel" "Mario" "Olga"
## [12,] "Adriana" "Angel" "Augusto" "Daniel" "Mario" "Paty"
## [13,] "Adriana" "Angel" "Augusto" "Daniel" "Mary" "Olga"
## [14,] "Adriana" "Angel" "Augusto" "Daniel" "Mary" "Paty"
## [15,] "Adriana" "Angel" "Augusto" "Daniel" "Olga" "Paty"
## [16,] "Adriana" "Angel" "Augusto" "Jesabel" "Jonhatan" "Mario"
## [17,] "Adriana" "Angel" "Augusto" "Jesabel" "Jonhatan" "Mary"
## [18,] "Adriana" "Angel" "Augusto" "Jesabel" "Jonhatan" "Olga"
## [19,] "Adriana" "Angel" "Augusto" "Jesabel" "Jonhatan" "Paty"
## [20,] "Adriana" "Angel" "Augusto" "Jesabel" "Mario" "Mary"
## [21,] "Adriana" "Angel" "Augusto" "Jesabel" "Mario" "Olga"
## [22,] "Adriana" "Angel" "Augusto" "Jesabel" "Mario" "Paty"
## [23,] "Adriana" "Angel" "Augusto" "Jesabel" "Mary" "Olga"
## [24,] "Adriana" "Angel" "Augusto" "Jesabel" "Mary" "Paty"
## [25,] "Adriana" "Angel" "Augusto" "Jesabel" "Olga" "Paty"
## [26,] "Adriana" "Angel" "Augusto" "Jonhatan" "Mario" "Mary"
## [27,] "Adriana" "Angel" "Augusto" "Jonhatan" "Mario" "Olga"
## [28,] "Adriana" "Angel" "Augusto" "Jonhatan" "Mario" "Paty"
## [29,] "Adriana" "Angel" "Augusto" "Jonhatan" "Mary" "Olga"
## [30,] "Adriana" "Angel" "Augusto" "Jonhatan" "Mary" "Paty"
## [31,] "Adriana" "Angel" "Augusto" "Jonhatan" "Olga" "Paty"
## [32,] "Adriana" "Angel" "Augusto" "Mario" "Mary" "Olga"
## [33,] "Adriana" "Angel" "Augusto" "Mario" "Mary" "Paty"
## [34,] "Adriana" "Angel" "Augusto" "Mario" "Olga" "Paty"
## [35,] "Adriana" "Angel" "Augusto" "Mary" "Olga" "Paty"
## [36,] "Adriana" "Angel" "Daniel" "Jesabel" "Jonhatan" "Mario"
## [37,] "Adriana" "Angel" "Daniel" "Jesabel" "Jonhatan" "Mary"
## [38,] "Adriana" "Angel" "Daniel" "Jesabel" "Jonhatan" "Olga"
## [39,] "Adriana" "Angel" "Daniel" "Jesabel" "Jonhatan" "Paty"
## [40,] "Adriana" "Angel" "Daniel" "Jesabel" "Mario" "Mary"
## [41,] "Adriana" "Angel" "Daniel" "Jesabel" "Mario" "Olga"
## [42,] "Adriana" "Angel" "Daniel" "Jesabel" "Mario" "Paty"
## [43,] "Adriana" "Angel" "Daniel" "Jesabel" "Mary" "Olga"
## [44,] "Adriana" "Angel" "Daniel" "Jesabel" "Mary" "Paty"
## [45,] "Adriana" "Angel" "Daniel" "Jesabel" "Olga" "Paty"
## [46,] "Adriana" "Angel" "Daniel" "Jonhatan" "Mario" "Mary"
## [47,] "Adriana" "Angel" "Daniel" "Jonhatan" "Mario" "Olga"
## [48,] "Adriana" "Angel" "Daniel" "Jonhatan" "Mario" "Paty"
## [49,] "Adriana" "Angel" "Daniel" "Jonhatan" "Mary" "Olga"
## [50,] "Adriana" "Angel" "Daniel" "Jonhatan" "Mary" "Paty"
## [51,] "Adriana" "Angel" "Daniel" "Jonhatan" "Olga" "Paty"
## [52,] "Adriana" "Angel" "Daniel" "Mario" "Mary" "Olga"
## [53,] "Adriana" "Angel" "Daniel" "Mario" "Mary" "Paty"
## [54,] "Adriana" "Angel" "Daniel" "Mario" "Olga" "Paty"
## [55,] "Adriana" "Angel" "Daniel" "Mary" "Olga" "Paty"
## [56,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Mario" "Mary"
## [57,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Mario" "Olga"
## [58,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Mario" "Paty"
## [59,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Mary" "Olga"
## [60,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Mary" "Paty"
## [61,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Olga" "Paty"
## [62,] "Adriana" "Angel" "Jesabel" "Mario" "Mary" "Olga"
## [63,] "Adriana" "Angel" "Jesabel" "Mario" "Mary" "Paty"
## [64,] "Adriana" "Angel" "Jesabel" "Mario" "Olga" "Paty"
## [65,] "Adriana" "Angel" "Jesabel" "Mary" "Olga" "Paty"
## [66,] "Adriana" "Angel" "Jonhatan" "Mario" "Mary" "Olga"
## [67,] "Adriana" "Angel" "Jonhatan" "Mario" "Mary" "Paty"
## [68,] "Adriana" "Angel" "Jonhatan" "Mario" "Olga" "Paty"
## [69,] "Adriana" "Angel" "Jonhatan" "Mary" "Olga" "Paty"
## [70,] "Adriana" "Angel" "Mario" "Mary" "Olga" "Paty"
## [71,] "Adriana" "Augusto" "Daniel" "Jesabel" "Jonhatan" "Mario"
## [72,] "Adriana" "Augusto" "Daniel" "Jesabel" "Jonhatan" "Mary"
## [73,] "Adriana" "Augusto" "Daniel" "Jesabel" "Jonhatan" "Olga"
## [74,] "Adriana" "Augusto" "Daniel" "Jesabel" "Jonhatan" "Paty"
## [75,] "Adriana" "Augusto" "Daniel" "Jesabel" "Mario" "Mary"
## [76,] "Adriana" "Augusto" "Daniel" "Jesabel" "Mario" "Olga"
## [77,] "Adriana" "Augusto" "Daniel" "Jesabel" "Mario" "Paty"
## [78,] "Adriana" "Augusto" "Daniel" "Jesabel" "Mary" "Olga"
## [79,] "Adriana" "Augusto" "Daniel" "Jesabel" "Mary" "Paty"
## [80,] "Adriana" "Augusto" "Daniel" "Jesabel" "Olga" "Paty"
## [81,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Mario" "Mary"
## [82,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Mario" "Olga"
## [83,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Mario" "Paty"
## [84,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Mary" "Olga"
## [85,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Mary" "Paty"
## [86,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Olga" "Paty"
## [87,] "Adriana" "Augusto" "Daniel" "Mario" "Mary" "Olga"
## [88,] "Adriana" "Augusto" "Daniel" "Mario" "Mary" "Paty"
## [89,] "Adriana" "Augusto" "Daniel" "Mario" "Olga" "Paty"
## [90,] "Adriana" "Augusto" "Daniel" "Mary" "Olga" "Paty"
## [91,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Mario" "Mary"
## [92,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Mario" "Olga"
## [93,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Mario" "Paty"
## [94,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Mary" "Olga"
## [95,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Mary" "Paty"
## [96,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Olga" "Paty"
## [97,] "Adriana" "Augusto" "Jesabel" "Mario" "Mary" "Olga"
## [98,] "Adriana" "Augusto" "Jesabel" "Mario" "Mary" "Paty"
## [99,] "Adriana" "Augusto" "Jesabel" "Mario" "Olga" "Paty"
## [100,] "Adriana" "Augusto" "Jesabel" "Mary" "Olga" "Paty"
## [101,] "Adriana" "Augusto" "Jonhatan" "Mario" "Mary" "Olga"
## [102,] "Adriana" "Augusto" "Jonhatan" "Mario" "Mary" "Paty"
## [103,] "Adriana" "Augusto" "Jonhatan" "Mario" "Olga" "Paty"
## [104,] "Adriana" "Augusto" "Jonhatan" "Mary" "Olga" "Paty"
## [105,] "Adriana" "Augusto" "Mario" "Mary" "Olga" "Paty"
## [106,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Mario" "Mary"
## [107,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Mario" "Olga"
## [108,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Mario" "Paty"
## [109,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Mary" "Olga"
## [110,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Mary" "Paty"
## [111,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Olga" "Paty"
## [112,] "Adriana" "Daniel" "Jesabel" "Mario" "Mary" "Olga"
## [113,] "Adriana" "Daniel" "Jesabel" "Mario" "Mary" "Paty"
## [114,] "Adriana" "Daniel" "Jesabel" "Mario" "Olga" "Paty"
## [115,] "Adriana" "Daniel" "Jesabel" "Mary" "Olga" "Paty"
## [116,] "Adriana" "Daniel" "Jonhatan" "Mario" "Mary" "Olga"
## [117,] "Adriana" "Daniel" "Jonhatan" "Mario" "Mary" "Paty"
## [118,] "Adriana" "Daniel" "Jonhatan" "Mario" "Olga" "Paty"
## [119,] "Adriana" "Daniel" "Jonhatan" "Mary" "Olga" "Paty"
## [120,] "Adriana" "Daniel" "Mario" "Mary" "Olga" "Paty"
## [121,] "Adriana" "Jesabel" "Jonhatan" "Mario" "Mary" "Olga"
## [122,] "Adriana" "Jesabel" "Jonhatan" "Mario" "Mary" "Paty"
## [123,] "Adriana" "Jesabel" "Jonhatan" "Mario" "Olga" "Paty"
## [124,] "Adriana" "Jesabel" "Jonhatan" "Mary" "Olga" "Paty"
## [125,] "Adriana" "Jesabel" "Mario" "Mary" "Olga" "Paty"
## [126,] "Adriana" "Jonhatan" "Mario" "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" "Angel" "Augusto" "Daniel" "Jesabel" "Jonhatan"
## [2,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Mario"
## [3,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Mary"
## [4,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Olga"
## [5,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Paty"
## [6,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Mario"
## [7,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Mary"
## [8,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Olga"
## [9,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Paty"
## [10,] "Adriana" "Angel" "Augusto" "Daniel" "Mario" "Mary"
## [11,] "Adriana" "Angel" "Augusto" "Daniel" "Mario" "Olga"
## [12,] "Adriana" "Angel" "Augusto" "Daniel" "Mario" "Paty"
## [13,] "Adriana" "Angel" "Augusto" "Daniel" "Mary" "Olga"
## [14,] "Adriana" "Angel" "Augusto" "Daniel" "Mary" "Paty"
## [15,] "Adriana" "Angel" "Augusto" "Daniel" "Olga" "Paty"
## [16,] "Adriana" "Angel" "Augusto" "Jesabel" "Jonhatan" "Mario"
## [17,] "Adriana" "Angel" "Augusto" "Jesabel" "Jonhatan" "Mary"
## [18,] "Adriana" "Angel" "Augusto" "Jesabel" "Jonhatan" "Olga"
## [19,] "Adriana" "Angel" "Augusto" "Jesabel" "Jonhatan" "Paty"
## [20,] "Adriana" "Angel" "Augusto" "Jesabel" "Mario" "Mary"
## [21,] "Adriana" "Angel" "Augusto" "Jesabel" "Mario" "Olga"
## [22,] "Adriana" "Angel" "Augusto" "Jesabel" "Mario" "Paty"
## [23,] "Adriana" "Angel" "Augusto" "Jesabel" "Mary" "Olga"
## [24,] "Adriana" "Angel" "Augusto" "Jesabel" "Mary" "Paty"
## [25,] "Adriana" "Angel" "Augusto" "Jesabel" "Olga" "Paty"
## [26,] "Adriana" "Angel" "Augusto" "Jonhatan" "Mario" "Mary"
## [27,] "Adriana" "Angel" "Augusto" "Jonhatan" "Mario" "Olga"
## [28,] "Adriana" "Angel" "Augusto" "Jonhatan" "Mario" "Paty"
## [29,] "Adriana" "Angel" "Augusto" "Jonhatan" "Mary" "Olga"
## [30,] "Adriana" "Angel" "Augusto" "Jonhatan" "Mary" "Paty"
## [31,] "Adriana" "Angel" "Augusto" "Jonhatan" "Olga" "Paty"
## [32,] "Adriana" "Angel" "Augusto" "Mario" "Mary" "Olga"
## [33,] "Adriana" "Angel" "Augusto" "Mario" "Mary" "Paty"
## [34,] "Adriana" "Angel" "Augusto" "Mario" "Olga" "Paty"
## [35,] "Adriana" "Angel" "Augusto" "Mary" "Olga" "Paty"
## [36,] "Adriana" "Angel" "Daniel" "Jesabel" "Jonhatan" "Mario"
## [37,] "Adriana" "Angel" "Daniel" "Jesabel" "Jonhatan" "Mary"
## [38,] "Adriana" "Angel" "Daniel" "Jesabel" "Jonhatan" "Olga"
## [39,] "Adriana" "Angel" "Daniel" "Jesabel" "Jonhatan" "Paty"
## [40,] "Adriana" "Angel" "Daniel" "Jesabel" "Mario" "Mary"
## [41,] "Adriana" "Angel" "Daniel" "Jesabel" "Mario" "Olga"
## [42,] "Adriana" "Angel" "Daniel" "Jesabel" "Mario" "Paty"
## [43,] "Adriana" "Angel" "Daniel" "Jesabel" "Mary" "Olga"
## [44,] "Adriana" "Angel" "Daniel" "Jesabel" "Mary" "Paty"
## [45,] "Adriana" "Angel" "Daniel" "Jesabel" "Olga" "Paty"
## [46,] "Adriana" "Angel" "Daniel" "Jonhatan" "Mario" "Mary"
## [47,] "Adriana" "Angel" "Daniel" "Jonhatan" "Mario" "Olga"
## [48,] "Adriana" "Angel" "Daniel" "Jonhatan" "Mario" "Paty"
## [49,] "Adriana" "Angel" "Daniel" "Jonhatan" "Mary" "Olga"
## [50,] "Adriana" "Angel" "Daniel" "Jonhatan" "Mary" "Paty"
## [51,] "Adriana" "Angel" "Daniel" "Jonhatan" "Olga" "Paty"
## [52,] "Adriana" "Angel" "Daniel" "Mario" "Mary" "Olga"
## [53,] "Adriana" "Angel" "Daniel" "Mario" "Mary" "Paty"
## [54,] "Adriana" "Angel" "Daniel" "Mario" "Olga" "Paty"
## [55,] "Adriana" "Angel" "Daniel" "Mary" "Olga" "Paty"
## [56,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Mario" "Mary"
## [57,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Mario" "Olga"
## [58,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Mario" "Paty"
## [59,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Mary" "Olga"
## [60,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Mary" "Paty"
## [61,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Olga" "Paty"
## [62,] "Adriana" "Angel" "Jesabel" "Mario" "Mary" "Olga"
## [63,] "Adriana" "Angel" "Jesabel" "Mario" "Mary" "Paty"
## [64,] "Adriana" "Angel" "Jesabel" "Mario" "Olga" "Paty"
## [65,] "Adriana" "Angel" "Jesabel" "Mary" "Olga" "Paty"
## [66,] "Adriana" "Angel" "Jonhatan" "Mario" "Mary" "Olga"
## [67,] "Adriana" "Angel" "Jonhatan" "Mario" "Mary" "Paty"
## [68,] "Adriana" "Angel" "Jonhatan" "Mario" "Olga" "Paty"
## [69,] "Adriana" "Angel" "Jonhatan" "Mary" "Olga" "Paty"
## [70,] "Adriana" "Angel" "Mario" "Mary" "Olga" "Paty"
## [71,] "Adriana" "Augusto" "Daniel" "Jesabel" "Jonhatan" "Mario"
## [72,] "Adriana" "Augusto" "Daniel" "Jesabel" "Jonhatan" "Mary"
## [73,] "Adriana" "Augusto" "Daniel" "Jesabel" "Jonhatan" "Olga"
## [74,] "Adriana" "Augusto" "Daniel" "Jesabel" "Jonhatan" "Paty"
## [75,] "Adriana" "Augusto" "Daniel" "Jesabel" "Mario" "Mary"
## [76,] "Adriana" "Augusto" "Daniel" "Jesabel" "Mario" "Olga"
## [77,] "Adriana" "Augusto" "Daniel" "Jesabel" "Mario" "Paty"
## [78,] "Adriana" "Augusto" "Daniel" "Jesabel" "Mary" "Olga"
## [79,] "Adriana" "Augusto" "Daniel" "Jesabel" "Mary" "Paty"
## [80,] "Adriana" "Augusto" "Daniel" "Jesabel" "Olga" "Paty"
## [81,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Mario" "Mary"
## [82,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Mario" "Olga"
## [83,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Mario" "Paty"
## [84,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Mary" "Olga"
## [85,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Mary" "Paty"
## [86,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Olga" "Paty"
## [87,] "Adriana" "Augusto" "Daniel" "Mario" "Mary" "Olga"
## [88,] "Adriana" "Augusto" "Daniel" "Mario" "Mary" "Paty"
## [89,] "Adriana" "Augusto" "Daniel" "Mario" "Olga" "Paty"
## [90,] "Adriana" "Augusto" "Daniel" "Mary" "Olga" "Paty"
## [91,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Mario" "Mary"
## [92,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Mario" "Olga"
## [93,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Mario" "Paty"
## [94,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Mary" "Olga"
## [95,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Mary" "Paty"
## [96,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Olga" "Paty"
## [97,] "Adriana" "Augusto" "Jesabel" "Mario" "Mary" "Olga"
## [98,] "Adriana" "Augusto" "Jesabel" "Mario" "Mary" "Paty"
## [99,] "Adriana" "Augusto" "Jesabel" "Mario" "Olga" "Paty"
## [100,] "Adriana" "Augusto" "Jesabel" "Mary" "Olga" "Paty"
## [101,] "Adriana" "Augusto" "Jonhatan" "Mario" "Mary" "Olga"
## [102,] "Adriana" "Augusto" "Jonhatan" "Mario" "Mary" "Paty"
## [103,] "Adriana" "Augusto" "Jonhatan" "Mario" "Olga" "Paty"
## [104,] "Adriana" "Augusto" "Jonhatan" "Mary" "Olga" "Paty"
## [105,] "Adriana" "Augusto" "Mario" "Mary" "Olga" "Paty"
## [106,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Mario" "Mary"
## [107,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Mario" "Olga"
## [108,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Mario" "Paty"
## [109,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Mary" "Olga"
## [110,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Mary" "Paty"
## [111,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Olga" "Paty"
## [112,] "Adriana" "Daniel" "Jesabel" "Mario" "Mary" "Olga"
## [113,] "Adriana" "Daniel" "Jesabel" "Mario" "Mary" "Paty"
## [114,] "Adriana" "Daniel" "Jesabel" "Mario" "Olga" "Paty"
## [115,] "Adriana" "Daniel" "Jesabel" "Mary" "Olga" "Paty"
## [116,] "Adriana" "Daniel" "Jonhatan" "Mario" "Mary" "Olga"
## [117,] "Adriana" "Daniel" "Jonhatan" "Mario" "Mary" "Paty"
## [118,] "Adriana" "Daniel" "Jonhatan" "Mario" "Olga" "Paty"
## [119,] "Adriana" "Daniel" "Jonhatan" "Mary" "Olga" "Paty"
## [120,] "Adriana" "Daniel" "Mario" "Mary" "Olga" "Paty"
## [121,] "Adriana" "Jesabel" "Jonhatan" "Mario" "Mary" "Olga"
## [122,] "Adriana" "Jesabel" "Jonhatan" "Mario" "Mary" "Paty"
## [123,] "Adriana" "Jesabel" "Jonhatan" "Mario" "Olga" "Paty"
## [124,] "Adriana" "Jesabel" "Jonhatan" "Mary" "Olga" "Paty"
## [125,] "Adriana" "Jesabel" "Mario" "Mary" "Olga" "Paty"
## [126,] "Adriana" "Jonhatan" "Mario" "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" "Angel" "Augusto" "Daniel" "Jesabel" "Paty"
## [2,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Paty"
## [3,] "Adriana" "Angel" "Augusto" "Daniel" "Mario" "Paty"
## [4,] "Adriana" "Angel" "Augusto" "Daniel" "Mary" "Paty"
## [5,] "Adriana" "Angel" "Augusto" "Daniel" "Olga" "Paty"
## [6,] "Adriana" "Angel" "Augusto" "Jesabel" "Jonhatan" "Paty"
## [7,] "Adriana" "Angel" "Augusto" "Jesabel" "Mario" "Paty"
## [8,] "Adriana" "Angel" "Augusto" "Jesabel" "Mary" "Paty"
## [9,] "Adriana" "Angel" "Augusto" "Jesabel" "Olga" "Paty"
## [10,] "Adriana" "Angel" "Augusto" "Jonhatan" "Mario" "Paty"
## [11,] "Adriana" "Angel" "Augusto" "Jonhatan" "Mary" "Paty"
## [12,] "Adriana" "Angel" "Augusto" "Jonhatan" "Olga" "Paty"
## [13,] "Adriana" "Angel" "Augusto" "Mario" "Mary" "Paty"
## [14,] "Adriana" "Angel" "Augusto" "Mario" "Olga" "Paty"
## [15,] "Adriana" "Angel" "Augusto" "Mary" "Olga" "Paty"
## [16,] "Adriana" "Angel" "Daniel" "Jesabel" "Jonhatan" "Paty"
## [17,] "Adriana" "Angel" "Daniel" "Jesabel" "Mario" "Paty"
## [18,] "Adriana" "Angel" "Daniel" "Jesabel" "Mary" "Paty"
## [19,] "Adriana" "Angel" "Daniel" "Jesabel" "Olga" "Paty"
## [20,] "Adriana" "Angel" "Daniel" "Jonhatan" "Mario" "Paty"
## [21,] "Adriana" "Angel" "Daniel" "Jonhatan" "Mary" "Paty"
## [22,] "Adriana" "Angel" "Daniel" "Jonhatan" "Olga" "Paty"
## [23,] "Adriana" "Angel" "Daniel" "Mario" "Mary" "Paty"
## [24,] "Adriana" "Angel" "Daniel" "Mario" "Olga" "Paty"
## [25,] "Adriana" "Angel" "Daniel" "Mary" "Olga" "Paty"
## [26,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Mario" "Paty"
## [27,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Mary" "Paty"
## [28,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Olga" "Paty"
## [29,] "Adriana" "Angel" "Jesabel" "Mario" "Mary" "Paty"
## [30,] "Adriana" "Angel" "Jesabel" "Mario" "Olga" "Paty"
## [31,] "Adriana" "Angel" "Jesabel" "Mary" "Olga" "Paty"
## [32,] "Adriana" "Angel" "Jonhatan" "Mario" "Mary" "Paty"
## [33,] "Adriana" "Angel" "Jonhatan" "Mario" "Olga" "Paty"
## [34,] "Adriana" "Angel" "Jonhatan" "Mary" "Olga" "Paty"
## [35,] "Adriana" "Angel" "Mario" "Mary" "Olga" "Paty"
## [36,] "Adriana" "Augusto" "Daniel" "Jesabel" "Jonhatan" "Paty"
## [37,] "Adriana" "Augusto" "Daniel" "Jesabel" "Mario" "Paty"
## [38,] "Adriana" "Augusto" "Daniel" "Jesabel" "Mary" "Paty"
## [39,] "Adriana" "Augusto" "Daniel" "Jesabel" "Olga" "Paty"
## [40,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Mario" "Paty"
## [41,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Mary" "Paty"
## [42,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Olga" "Paty"
## [43,] "Adriana" "Augusto" "Daniel" "Mario" "Mary" "Paty"
## [44,] "Adriana" "Augusto" "Daniel" "Mario" "Olga" "Paty"
## [45,] "Adriana" "Augusto" "Daniel" "Mary" "Olga" "Paty"
## [46,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Mario" "Paty"
## [47,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Mary" "Paty"
## [48,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Olga" "Paty"
## [49,] "Adriana" "Augusto" "Jesabel" "Mario" "Mary" "Paty"
## [50,] "Adriana" "Augusto" "Jesabel" "Mario" "Olga" "Paty"
## [51,] "Adriana" "Augusto" "Jesabel" "Mary" "Olga" "Paty"
## [52,] "Adriana" "Augusto" "Jonhatan" "Mario" "Mary" "Paty"
## [53,] "Adriana" "Augusto" "Jonhatan" "Mario" "Olga" "Paty"
## [54,] "Adriana" "Augusto" "Jonhatan" "Mary" "Olga" "Paty"
## [55,] "Adriana" "Augusto" "Mario" "Mary" "Olga" "Paty"
## [56,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Mario" "Paty"
## [57,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Mary" "Paty"
## [58,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Olga" "Paty"
## [59,] "Adriana" "Daniel" "Jesabel" "Mario" "Mary" "Paty"
## [60,] "Adriana" "Daniel" "Jesabel" "Mario" "Olga" "Paty"
## [61,] "Adriana" "Daniel" "Jesabel" "Mary" "Olga" "Paty"
## [62,] "Adriana" "Daniel" "Jonhatan" "Mario" "Mary" "Paty"
## [63,] "Adriana" "Daniel" "Jonhatan" "Mario" "Olga" "Paty"
## [64,] "Adriana" "Daniel" "Jonhatan" "Mary" "Olga" "Paty"
## [65,] "Adriana" "Daniel" "Mario" "Mary" "Olga" "Paty"
## [66,] "Adriana" "Jesabel" "Jonhatan" "Mario" "Mary" "Paty"
## [67,] "Adriana" "Jesabel" "Jonhatan" "Mario" "Olga" "Paty"
## [68,] "Adriana" "Jesabel" "Jonhatan" "Mary" "Olga" "Paty"
## [69,] "Adriana" "Jesabel" "Mario" "Mary" "Olga" "Paty"
## [70,] "Adriana" "Jonhatan" "Mario" "Mary" "Olga" "Paty"
## [71,] "Angel" "Augusto" "Daniel" "Jesabel" "Jonhatan" "Paty"
## [72,] "Angel" "Augusto" "Daniel" "Jesabel" "Mario" "Paty"
## [73,] "Angel" "Augusto" "Daniel" "Jesabel" "Mary" "Paty"
## [74,] "Angel" "Augusto" "Daniel" "Jesabel" "Olga" "Paty"
## [75,] "Angel" "Augusto" "Daniel" "Jonhatan" "Mario" "Paty"
## [76,] "Angel" "Augusto" "Daniel" "Jonhatan" "Mary" "Paty"
## [77,] "Angel" "Augusto" "Daniel" "Jonhatan" "Olga" "Paty"
## [78,] "Angel" "Augusto" "Daniel" "Mario" "Mary" "Paty"
## [79,] "Angel" "Augusto" "Daniel" "Mario" "Olga" "Paty"
## [80,] "Angel" "Augusto" "Daniel" "Mary" "Olga" "Paty"
## [81,] "Angel" "Augusto" "Jesabel" "Jonhatan" "Mario" "Paty"
## [82,] "Angel" "Augusto" "Jesabel" "Jonhatan" "Mary" "Paty"
## [83,] "Angel" "Augusto" "Jesabel" "Jonhatan" "Olga" "Paty"
## [84,] "Angel" "Augusto" "Jesabel" "Mario" "Mary" "Paty"
## [85,] "Angel" "Augusto" "Jesabel" "Mario" "Olga" "Paty"
## [86,] "Angel" "Augusto" "Jesabel" "Mary" "Olga" "Paty"
## [87,] "Angel" "Augusto" "Jonhatan" "Mario" "Mary" "Paty"
## [88,] "Angel" "Augusto" "Jonhatan" "Mario" "Olga" "Paty"
## [89,] "Angel" "Augusto" "Jonhatan" "Mary" "Olga" "Paty"
## [90,] "Angel" "Augusto" "Mario" "Mary" "Olga" "Paty"
## [91,] "Angel" "Daniel" "Jesabel" "Jonhatan" "Mario" "Paty"
## [92,] "Angel" "Daniel" "Jesabel" "Jonhatan" "Mary" "Paty"
## [93,] "Angel" "Daniel" "Jesabel" "Jonhatan" "Olga" "Paty"
## [94,] "Angel" "Daniel" "Jesabel" "Mario" "Mary" "Paty"
## [95,] "Angel" "Daniel" "Jesabel" "Mario" "Olga" "Paty"
## [96,] "Angel" "Daniel" "Jesabel" "Mary" "Olga" "Paty"
## [97,] "Angel" "Daniel" "Jonhatan" "Mario" "Mary" "Paty"
## [98,] "Angel" "Daniel" "Jonhatan" "Mario" "Olga" "Paty"
## [99,] "Angel" "Daniel" "Jonhatan" "Mary" "Olga" "Paty"
## [100,] "Angel" "Daniel" "Mario" "Mary" "Olga" "Paty"
## [101,] "Angel" "Jesabel" "Jonhatan" "Mario" "Mary" "Paty"
## [102,] "Angel" "Jesabel" "Jonhatan" "Mario" "Olga" "Paty"
## [103,] "Angel" "Jesabel" "Jonhatan" "Mary" "Olga" "Paty"
## [104,] "Angel" "Jesabel" "Mario" "Mary" "Olga" "Paty"
## [105,] "Angel" "Jonhatan" "Mario" "Mary" "Olga" "Paty"
## [106,] "Augusto" "Daniel" "Jesabel" "Jonhatan" "Mario" "Paty"
## [107,] "Augusto" "Daniel" "Jesabel" "Jonhatan" "Mary" "Paty"
## [108,] "Augusto" "Daniel" "Jesabel" "Jonhatan" "Olga" "Paty"
## [109,] "Augusto" "Daniel" "Jesabel" "Mario" "Mary" "Paty"
## [110,] "Augusto" "Daniel" "Jesabel" "Mario" "Olga" "Paty"
## [111,] "Augusto" "Daniel" "Jesabel" "Mary" "Olga" "Paty"
## [112,] "Augusto" "Daniel" "Jonhatan" "Mario" "Mary" "Paty"
## [113,] "Augusto" "Daniel" "Jonhatan" "Mario" "Olga" "Paty"
## [114,] "Augusto" "Daniel" "Jonhatan" "Mary" "Olga" "Paty"
## [115,] "Augusto" "Daniel" "Mario" "Mary" "Olga" "Paty"
## [116,] "Augusto" "Jesabel" "Jonhatan" "Mario" "Mary" "Paty"
## [117,] "Augusto" "Jesabel" "Jonhatan" "Mario" "Olga" "Paty"
## [118,] "Augusto" "Jesabel" "Jonhatan" "Mary" "Olga" "Paty"
## [119,] "Augusto" "Jesabel" "Mario" "Mary" "Olga" "Paty"
## [120,] "Augusto" "Jonhatan" "Mario" "Mary" "Olga" "Paty"
## [121,] "Daniel" "Jesabel" "Jonhatan" "Mario" "Mary" "Paty"
## [122,] "Daniel" "Jesabel" "Jonhatan" "Mario" "Olga" "Paty"
## [123,] "Daniel" "Jesabel" "Jonhatan" "Mary" "Olga" "Paty"
## [124,] "Daniel" "Jesabel" "Mario" "Mary" "Olga" "Paty"
## [125,] "Daniel" "Jonhatan" "Mario" "Mary" "Olga" "Paty"
## [126,] "Jesabel" "Jonhatan" "Mario" "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" "Angel" "Augusto" "Daniel" "Jesabel" "Olga"
## [2,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Olga"
## [3,] "Adriana" "Angel" "Augusto" "Daniel" "Mario" "Olga"
## [4,] "Adriana" "Angel" "Augusto" "Daniel" "Mary" "Olga"
## [5,] "Adriana" "Angel" "Augusto" "Daniel" "Olga" "Paty"
## [6,] "Adriana" "Angel" "Augusto" "Jesabel" "Jonhatan" "Olga"
## [7,] "Adriana" "Angel" "Augusto" "Jesabel" "Mario" "Olga"
## [8,] "Adriana" "Angel" "Augusto" "Jesabel" "Mary" "Olga"
## [9,] "Adriana" "Angel" "Augusto" "Jesabel" "Olga" "Paty"
## [10,] "Adriana" "Angel" "Augusto" "Jonhatan" "Mario" "Olga"
## [11,] "Adriana" "Angel" "Augusto" "Jonhatan" "Mary" "Olga"
## [12,] "Adriana" "Angel" "Augusto" "Jonhatan" "Olga" "Paty"
## [13,] "Adriana" "Angel" "Augusto" "Mario" "Mary" "Olga"
## [14,] "Adriana" "Angel" "Augusto" "Mario" "Olga" "Paty"
## [15,] "Adriana" "Angel" "Augusto" "Mary" "Olga" "Paty"
## [16,] "Adriana" "Angel" "Daniel" "Jesabel" "Jonhatan" "Olga"
## [17,] "Adriana" "Angel" "Daniel" "Jesabel" "Mario" "Olga"
## [18,] "Adriana" "Angel" "Daniel" "Jesabel" "Mary" "Olga"
## [19,] "Adriana" "Angel" "Daniel" "Jesabel" "Olga" "Paty"
## [20,] "Adriana" "Angel" "Daniel" "Jonhatan" "Mario" "Olga"
## [21,] "Adriana" "Angel" "Daniel" "Jonhatan" "Mary" "Olga"
## [22,] "Adriana" "Angel" "Daniel" "Jonhatan" "Olga" "Paty"
## [23,] "Adriana" "Angel" "Daniel" "Mario" "Mary" "Olga"
## [24,] "Adriana" "Angel" "Daniel" "Mario" "Olga" "Paty"
## [25,] "Adriana" "Angel" "Daniel" "Mary" "Olga" "Paty"
## [26,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Mario" "Olga"
## [27,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Mary" "Olga"
## [28,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Olga" "Paty"
## [29,] "Adriana" "Angel" "Jesabel" "Mario" "Mary" "Olga"
## [30,] "Adriana" "Angel" "Jesabel" "Mario" "Olga" "Paty"
## [31,] "Adriana" "Angel" "Jesabel" "Mary" "Olga" "Paty"
## [32,] "Adriana" "Angel" "Jonhatan" "Mario" "Mary" "Olga"
## [33,] "Adriana" "Angel" "Jonhatan" "Mario" "Olga" "Paty"
## [34,] "Adriana" "Angel" "Jonhatan" "Mary" "Olga" "Paty"
## [35,] "Adriana" "Angel" "Mario" "Mary" "Olga" "Paty"
## [36,] "Adriana" "Augusto" "Daniel" "Jesabel" "Jonhatan" "Olga"
## [37,] "Adriana" "Augusto" "Daniel" "Jesabel" "Mario" "Olga"
## [38,] "Adriana" "Augusto" "Daniel" "Jesabel" "Mary" "Olga"
## [39,] "Adriana" "Augusto" "Daniel" "Jesabel" "Olga" "Paty"
## [40,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Mario" "Olga"
## [41,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Mary" "Olga"
## [42,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Olga" "Paty"
## [43,] "Adriana" "Augusto" "Daniel" "Mario" "Mary" "Olga"
## [44,] "Adriana" "Augusto" "Daniel" "Mario" "Olga" "Paty"
## [45,] "Adriana" "Augusto" "Daniel" "Mary" "Olga" "Paty"
## [46,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Mario" "Olga"
## [47,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Mary" "Olga"
## [48,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Olga" "Paty"
## [49,] "Adriana" "Augusto" "Jesabel" "Mario" "Mary" "Olga"
## [50,] "Adriana" "Augusto" "Jesabel" "Mario" "Olga" "Paty"
## [51,] "Adriana" "Augusto" "Jesabel" "Mary" "Olga" "Paty"
## [52,] "Adriana" "Augusto" "Jonhatan" "Mario" "Mary" "Olga"
## [53,] "Adriana" "Augusto" "Jonhatan" "Mario" "Olga" "Paty"
## [54,] "Adriana" "Augusto" "Jonhatan" "Mary" "Olga" "Paty"
## [55,] "Adriana" "Augusto" "Mario" "Mary" "Olga" "Paty"
## [56,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Mario" "Olga"
## [57,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Mary" "Olga"
## [58,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Olga" "Paty"
## [59,] "Adriana" "Daniel" "Jesabel" "Mario" "Mary" "Olga"
## [60,] "Adriana" "Daniel" "Jesabel" "Mario" "Olga" "Paty"
## [61,] "Adriana" "Daniel" "Jesabel" "Mary" "Olga" "Paty"
## [62,] "Adriana" "Daniel" "Jonhatan" "Mario" "Mary" "Olga"
## [63,] "Adriana" "Daniel" "Jonhatan" "Mario" "Olga" "Paty"
## [64,] "Adriana" "Daniel" "Jonhatan" "Mary" "Olga" "Paty"
## [65,] "Adriana" "Daniel" "Mario" "Mary" "Olga" "Paty"
## [66,] "Adriana" "Jesabel" "Jonhatan" "Mario" "Mary" "Olga"
## [67,] "Adriana" "Jesabel" "Jonhatan" "Mario" "Olga" "Paty"
## [68,] "Adriana" "Jesabel" "Jonhatan" "Mary" "Olga" "Paty"
## [69,] "Adriana" "Jesabel" "Mario" "Mary" "Olga" "Paty"
## [70,] "Adriana" "Jonhatan" "Mario" "Mary" "Olga" "Paty"
## [71,] "Angel" "Augusto" "Daniel" "Jesabel" "Jonhatan" "Olga"
## [72,] "Angel" "Augusto" "Daniel" "Jesabel" "Mario" "Olga"
## [73,] "Angel" "Augusto" "Daniel" "Jesabel" "Mary" "Olga"
## [74,] "Angel" "Augusto" "Daniel" "Jesabel" "Olga" "Paty"
## [75,] "Angel" "Augusto" "Daniel" "Jonhatan" "Mario" "Olga"
## [76,] "Angel" "Augusto" "Daniel" "Jonhatan" "Mary" "Olga"
## [77,] "Angel" "Augusto" "Daniel" "Jonhatan" "Olga" "Paty"
## [78,] "Angel" "Augusto" "Daniel" "Mario" "Mary" "Olga"
## [79,] "Angel" "Augusto" "Daniel" "Mario" "Olga" "Paty"
## [80,] "Angel" "Augusto" "Daniel" "Mary" "Olga" "Paty"
## [81,] "Angel" "Augusto" "Jesabel" "Jonhatan" "Mario" "Olga"
## [82,] "Angel" "Augusto" "Jesabel" "Jonhatan" "Mary" "Olga"
## [83,] "Angel" "Augusto" "Jesabel" "Jonhatan" "Olga" "Paty"
## [84,] "Angel" "Augusto" "Jesabel" "Mario" "Mary" "Olga"
## [85,] "Angel" "Augusto" "Jesabel" "Mario" "Olga" "Paty"
## [86,] "Angel" "Augusto" "Jesabel" "Mary" "Olga" "Paty"
## [87,] "Angel" "Augusto" "Jonhatan" "Mario" "Mary" "Olga"
## [88,] "Angel" "Augusto" "Jonhatan" "Mario" "Olga" "Paty"
## [89,] "Angel" "Augusto" "Jonhatan" "Mary" "Olga" "Paty"
## [90,] "Angel" "Augusto" "Mario" "Mary" "Olga" "Paty"
## [91,] "Angel" "Daniel" "Jesabel" "Jonhatan" "Mario" "Olga"
## [92,] "Angel" "Daniel" "Jesabel" "Jonhatan" "Mary" "Olga"
## [93,] "Angel" "Daniel" "Jesabel" "Jonhatan" "Olga" "Paty"
## [94,] "Angel" "Daniel" "Jesabel" "Mario" "Mary" "Olga"
## [95,] "Angel" "Daniel" "Jesabel" "Mario" "Olga" "Paty"
## [96,] "Angel" "Daniel" "Jesabel" "Mary" "Olga" "Paty"
## [97,] "Angel" "Daniel" "Jonhatan" "Mario" "Mary" "Olga"
## [98,] "Angel" "Daniel" "Jonhatan" "Mario" "Olga" "Paty"
## [99,] "Angel" "Daniel" "Jonhatan" "Mary" "Olga" "Paty"
## [100,] "Angel" "Daniel" "Mario" "Mary" "Olga" "Paty"
## [101,] "Angel" "Jesabel" "Jonhatan" "Mario" "Mary" "Olga"
## [102,] "Angel" "Jesabel" "Jonhatan" "Mario" "Olga" "Paty"
## [103,] "Angel" "Jesabel" "Jonhatan" "Mary" "Olga" "Paty"
## [104,] "Angel" "Jesabel" "Mario" "Mary" "Olga" "Paty"
## [105,] "Angel" "Jonhatan" "Mario" "Mary" "Olga" "Paty"
## [106,] "Augusto" "Daniel" "Jesabel" "Jonhatan" "Mario" "Olga"
## [107,] "Augusto" "Daniel" "Jesabel" "Jonhatan" "Mary" "Olga"
## [108,] "Augusto" "Daniel" "Jesabel" "Jonhatan" "Olga" "Paty"
## [109,] "Augusto" "Daniel" "Jesabel" "Mario" "Mary" "Olga"
## [110,] "Augusto" "Daniel" "Jesabel" "Mario" "Olga" "Paty"
## [111,] "Augusto" "Daniel" "Jesabel" "Mary" "Olga" "Paty"
## [112,] "Augusto" "Daniel" "Jonhatan" "Mario" "Mary" "Olga"
## [113,] "Augusto" "Daniel" "Jonhatan" "Mario" "Olga" "Paty"
## [114,] "Augusto" "Daniel" "Jonhatan" "Mary" "Olga" "Paty"
## [115,] "Augusto" "Daniel" "Mario" "Mary" "Olga" "Paty"
## [116,] "Augusto" "Jesabel" "Jonhatan" "Mario" "Mary" "Olga"
## [117,] "Augusto" "Jesabel" "Jonhatan" "Mario" "Olga" "Paty"
## [118,] "Augusto" "Jesabel" "Jonhatan" "Mary" "Olga" "Paty"
## [119,] "Augusto" "Jesabel" "Mario" "Mary" "Olga" "Paty"
## [120,] "Augusto" "Jonhatan" "Mario" "Mary" "Olga" "Paty"
## [121,] "Daniel" "Jesabel" "Jonhatan" "Mario" "Mary" "Olga"
## [122,] "Daniel" "Jesabel" "Jonhatan" "Mario" "Olga" "Paty"
## [123,] "Daniel" "Jesabel" "Jonhatan" "Mary" "Olga" "Paty"
## [124,] "Daniel" "Jesabel" "Mario" "Mary" "Olga" "Paty"
## [125,] "Daniel" "Jonhatan" "Mario" "Mary" "Olga" "Paty"
## [126,] "Jesabel" "Jonhatan" "Mario" "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" "Angel" "Augusto" "Daniel" "Jesabel" "Olga"
## [2,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Olga"
## [3,] "Adriana" "Angel" "Augusto" "Daniel" "Mario" "Olga"
## [4,] "Adriana" "Angel" "Augusto" "Daniel" "Mary" "Olga"
## [5,] "Adriana" "Angel" "Augusto" "Daniel" "Olga" "Paty"
## [6,] "Adriana" "Angel" "Augusto" "Jesabel" "Jonhatan" "Olga"
## [7,] "Adriana" "Angel" "Augusto" "Jesabel" "Mario" "Olga"
## [8,] "Adriana" "Angel" "Augusto" "Jesabel" "Mary" "Olga"
## [9,] "Adriana" "Angel" "Augusto" "Jesabel" "Olga" "Paty"
## [10,] "Adriana" "Angel" "Augusto" "Jonhatan" "Mario" "Olga"
## [11,] "Adriana" "Angel" "Augusto" "Jonhatan" "Mary" "Olga"
## [12,] "Adriana" "Angel" "Augusto" "Jonhatan" "Olga" "Paty"
## [13,] "Adriana" "Angel" "Augusto" "Mario" "Mary" "Olga"
## [14,] "Adriana" "Angel" "Augusto" "Mario" "Olga" "Paty"
## [15,] "Adriana" "Angel" "Augusto" "Mary" "Olga" "Paty"
## [16,] "Adriana" "Angel" "Daniel" "Jesabel" "Jonhatan" "Olga"
## [17,] "Adriana" "Angel" "Daniel" "Jesabel" "Mario" "Olga"
## [18,] "Adriana" "Angel" "Daniel" "Jesabel" "Mary" "Olga"
## [19,] "Adriana" "Angel" "Daniel" "Jesabel" "Olga" "Paty"
## [20,] "Adriana" "Angel" "Daniel" "Jonhatan" "Mario" "Olga"
## [21,] "Adriana" "Angel" "Daniel" "Jonhatan" "Mary" "Olga"
## [22,] "Adriana" "Angel" "Daniel" "Jonhatan" "Olga" "Paty"
## [23,] "Adriana" "Angel" "Daniel" "Mario" "Mary" "Olga"
## [24,] "Adriana" "Angel" "Daniel" "Mario" "Olga" "Paty"
## [25,] "Adriana" "Angel" "Daniel" "Mary" "Olga" "Paty"
## [26,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Mario" "Olga"
## [27,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Mary" "Olga"
## [28,] "Adriana" "Angel" "Jesabel" "Jonhatan" "Olga" "Paty"
## [29,] "Adriana" "Angel" "Jesabel" "Mario" "Mary" "Olga"
## [30,] "Adriana" "Angel" "Jesabel" "Mario" "Olga" "Paty"
## [31,] "Adriana" "Angel" "Jesabel" "Mary" "Olga" "Paty"
## [32,] "Adriana" "Angel" "Jonhatan" "Mario" "Mary" "Olga"
## [33,] "Adriana" "Angel" "Jonhatan" "Mario" "Olga" "Paty"
## [34,] "Adriana" "Angel" "Jonhatan" "Mary" "Olga" "Paty"
## [35,] "Adriana" "Angel" "Mario" "Mary" "Olga" "Paty"
## [36,] "Adriana" "Augusto" "Daniel" "Jesabel" "Jonhatan" "Olga"
## [37,] "Adriana" "Augusto" "Daniel" "Jesabel" "Mario" "Olga"
## [38,] "Adriana" "Augusto" "Daniel" "Jesabel" "Mary" "Olga"
## [39,] "Adriana" "Augusto" "Daniel" "Jesabel" "Olga" "Paty"
## [40,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Mario" "Olga"
## [41,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Mary" "Olga"
## [42,] "Adriana" "Augusto" "Daniel" "Jonhatan" "Olga" "Paty"
## [43,] "Adriana" "Augusto" "Daniel" "Mario" "Mary" "Olga"
## [44,] "Adriana" "Augusto" "Daniel" "Mario" "Olga" "Paty"
## [45,] "Adriana" "Augusto" "Daniel" "Mary" "Olga" "Paty"
## [46,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Mario" "Olga"
## [47,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Mary" "Olga"
## [48,] "Adriana" "Augusto" "Jesabel" "Jonhatan" "Olga" "Paty"
## [49,] "Adriana" "Augusto" "Jesabel" "Mario" "Mary" "Olga"
## [50,] "Adriana" "Augusto" "Jesabel" "Mario" "Olga" "Paty"
## [51,] "Adriana" "Augusto" "Jesabel" "Mary" "Olga" "Paty"
## [52,] "Adriana" "Augusto" "Jonhatan" "Mario" "Mary" "Olga"
## [53,] "Adriana" "Augusto" "Jonhatan" "Mario" "Olga" "Paty"
## [54,] "Adriana" "Augusto" "Jonhatan" "Mary" "Olga" "Paty"
## [55,] "Adriana" "Augusto" "Mario" "Mary" "Olga" "Paty"
## [56,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Mario" "Olga"
## [57,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Mary" "Olga"
## [58,] "Adriana" "Daniel" "Jesabel" "Jonhatan" "Olga" "Paty"
## [59,] "Adriana" "Daniel" "Jesabel" "Mario" "Mary" "Olga"
## [60,] "Adriana" "Daniel" "Jesabel" "Mario" "Olga" "Paty"
## [61,] "Adriana" "Daniel" "Jesabel" "Mary" "Olga" "Paty"
## [62,] "Adriana" "Daniel" "Jonhatan" "Mario" "Mary" "Olga"
## [63,] "Adriana" "Daniel" "Jonhatan" "Mario" "Olga" "Paty"
## [64,] "Adriana" "Daniel" "Jonhatan" "Mary" "Olga" "Paty"
## [65,] "Adriana" "Daniel" "Mario" "Mary" "Olga" "Paty"
## [66,] "Adriana" "Jesabel" "Jonhatan" "Mario" "Mary" "Olga"
## [67,] "Adriana" "Jesabel" "Jonhatan" "Mario" "Olga" "Paty"
## [68,] "Adriana" "Jesabel" "Jonhatan" "Mary" "Olga" "Paty"
## [69,] "Adriana" "Jesabel" "Mario" "Mary" "Olga" "Paty"
## [70,] "Adriana" "Jonhatan" "Mario" "Mary" "Olga" "Paty"
## [71,] "Angel" "Augusto" "Daniel" "Jesabel" "Jonhatan" "Olga"
## [72,] "Angel" "Augusto" "Daniel" "Jesabel" "Mario" "Olga"
## [73,] "Angel" "Augusto" "Daniel" "Jesabel" "Mary" "Olga"
## [74,] "Angel" "Augusto" "Daniel" "Jesabel" "Olga" "Paty"
## [75,] "Angel" "Augusto" "Daniel" "Jonhatan" "Mario" "Olga"
## [76,] "Angel" "Augusto" "Daniel" "Jonhatan" "Mary" "Olga"
## [77,] "Angel" "Augusto" "Daniel" "Jonhatan" "Olga" "Paty"
## [78,] "Angel" "Augusto" "Daniel" "Mario" "Mary" "Olga"
## [79,] "Angel" "Augusto" "Daniel" "Mario" "Olga" "Paty"
## [80,] "Angel" "Augusto" "Daniel" "Mary" "Olga" "Paty"
## [81,] "Angel" "Augusto" "Jesabel" "Jonhatan" "Mario" "Olga"
## [82,] "Angel" "Augusto" "Jesabel" "Jonhatan" "Mary" "Olga"
## [83,] "Angel" "Augusto" "Jesabel" "Jonhatan" "Olga" "Paty"
## [84,] "Angel" "Augusto" "Jesabel" "Mario" "Mary" "Olga"
## [85,] "Angel" "Augusto" "Jesabel" "Mario" "Olga" "Paty"
## [86,] "Angel" "Augusto" "Jesabel" "Mary" "Olga" "Paty"
## [87,] "Angel" "Augusto" "Jonhatan" "Mario" "Mary" "Olga"
## [88,] "Angel" "Augusto" "Jonhatan" "Mario" "Olga" "Paty"
## [89,] "Angel" "Augusto" "Jonhatan" "Mary" "Olga" "Paty"
## [90,] "Angel" "Augusto" "Mario" "Mary" "Olga" "Paty"
## [91,] "Angel" "Daniel" "Jesabel" "Jonhatan" "Mario" "Olga"
## [92,] "Angel" "Daniel" "Jesabel" "Jonhatan" "Mary" "Olga"
## [93,] "Angel" "Daniel" "Jesabel" "Jonhatan" "Olga" "Paty"
## [94,] "Angel" "Daniel" "Jesabel" "Mario" "Mary" "Olga"
## [95,] "Angel" "Daniel" "Jesabel" "Mario" "Olga" "Paty"
## [96,] "Angel" "Daniel" "Jesabel" "Mary" "Olga" "Paty"
## [97,] "Angel" "Daniel" "Jonhatan" "Mario" "Mary" "Olga"
## [98,] "Angel" "Daniel" "Jonhatan" "Mario" "Olga" "Paty"
## [99,] "Angel" "Daniel" "Jonhatan" "Mary" "Olga" "Paty"
## [100,] "Angel" "Daniel" "Mario" "Mary" "Olga" "Paty"
## [101,] "Angel" "Jesabel" "Jonhatan" "Mario" "Mary" "Olga"
## [102,] "Angel" "Jesabel" "Jonhatan" "Mario" "Olga" "Paty"
## [103,] "Angel" "Jesabel" "Jonhatan" "Mary" "Olga" "Paty"
## [104,] "Angel" "Jesabel" "Mario" "Mary" "Olga" "Paty"
## [105,] "Angel" "Jonhatan" "Mario" "Mary" "Olga" "Paty"
## [106,] "Augusto" "Daniel" "Jesabel" "Jonhatan" "Mario" "Olga"
## [107,] "Augusto" "Daniel" "Jesabel" "Jonhatan" "Mary" "Olga"
## [108,] "Augusto" "Daniel" "Jesabel" "Jonhatan" "Olga" "Paty"
## [109,] "Augusto" "Daniel" "Jesabel" "Mario" "Mary" "Olga"
## [110,] "Augusto" "Daniel" "Jesabel" "Mario" "Olga" "Paty"
## [111,] "Augusto" "Daniel" "Jesabel" "Mary" "Olga" "Paty"
## [112,] "Augusto" "Daniel" "Jonhatan" "Mario" "Mary" "Olga"
## [113,] "Augusto" "Daniel" "Jonhatan" "Mario" "Olga" "Paty"
## [114,] "Augusto" "Daniel" "Jonhatan" "Mary" "Olga" "Paty"
## [115,] "Augusto" "Daniel" "Mario" "Mary" "Olga" "Paty"
## [116,] "Augusto" "Jesabel" "Jonhatan" "Mario" "Mary" "Olga"
## [117,] "Augusto" "Jesabel" "Jonhatan" "Mario" "Olga" "Paty"
## [118,] "Augusto" "Jesabel" "Jonhatan" "Mary" "Olga" "Paty"
## [119,] "Augusto" "Jesabel" "Mario" "Mary" "Olga" "Paty"
## [120,] "Augusto" "Jonhatan" "Mario" "Mary" "Olga" "Paty"
## [121,] "Daniel" "Jesabel" "Jonhatan" "Mario" "Mary" "Olga"
## [122,] "Daniel" "Jesabel" "Jonhatan" "Mario" "Olga" "Paty"
## [123,] "Daniel" "Jesabel" "Jonhatan" "Mary" "Olga" "Paty"
## [124,] "Daniel" "Jesabel" "Mario" "Mary" "Olga" "Paty"
## [125,] "Daniel" "Jonhatan" "Mario" "Mary" "Olga" "Paty"
## [126,] "Jesabel" "Jonhatan" "Mario" "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" "Angel" "Augusto" "Mary" "Olga" "Paty"
## [2,] "Adriana" "Angel" "Daniel" "Mary" "Olga" "Paty"
## [3,] "Adriana" "Angel" "Jesabel" "Mary" "Olga" "Paty"
## [4,] "Adriana" "Angel" "Jonhatan" "Mary" "Olga" "Paty"
## [5,] "Adriana" "Angel" "Mario" "Mary" "Olga" "Paty"
## [6,] "Adriana" "Augusto" "Daniel" "Mary" "Olga" "Paty"
## [7,] "Adriana" "Augusto" "Jesabel" "Mary" "Olga" "Paty"
## [8,] "Adriana" "Augusto" "Jonhatan" "Mary" "Olga" "Paty"
## [9,] "Adriana" "Augusto" "Mario" "Mary" "Olga" "Paty"
## [10,] "Adriana" "Daniel" "Jesabel" "Mary" "Olga" "Paty"
## [11,] "Adriana" "Daniel" "Jonhatan" "Mary" "Olga" "Paty"
## [12,] "Adriana" "Daniel" "Mario" "Mary" "Olga" "Paty"
## [13,] "Adriana" "Jesabel" "Jonhatan" "Mary" "Olga" "Paty"
## [14,] "Adriana" "Jesabel" "Mario" "Mary" "Olga" "Paty"
## [15,] "Adriana" "Jonhatan" "Mario" "Mary" "Olga" "Paty"
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'),])
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Jonhatan"
## [2,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Mario"
## [3,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Mary"
## [4,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Olga"
## [5,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Paty"
## [6,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Jesabel"
tail(permutaciones[which(permutaciones[,1] == 'Adriana'),])
## [,1] [,2] [,3] [,4] [,5] [,6]
## [15115,] "Adriana" "Paty" "Olga" "Mary" "Jonhatan" "Mario"
## [15116,] "Adriana" "Paty" "Olga" "Mary" "Mario" "Angel"
## [15117,] "Adriana" "Paty" "Olga" "Mary" "Mario" "Augusto"
## [15118,] "Adriana" "Paty" "Olga" "Mary" "Mario" "Daniel"
## [15119,] "Adriana" "Paty" "Olga" "Mary" "Mario" "Jesabel"
## [15120,] "Adriana" "Paty" "Olga" "Mary" "Mario" "Jonhatan"
head(permutaciones[which(permutaciones[,1] == 'Adriana' | permutaciones[,2] == 'Adriana' | permutaciones[,3] == 'Adriana'),])
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Jonhatan"
## [2,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Mario"
## [3,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Mary"
## [4,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Olga"
## [5,] "Adriana" "Angel" "Augusto" "Daniel" "Jesabel" "Paty"
## [6,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Jesabel"
tail(permutaciones[which(permutaciones[,1] == 'Adriana' | permutaciones[,2] == 'Adriana' | permutaciones[,3] == 'Adriana'),])
## [,1] [,2] [,3] [,4] [,5] [,6]
## [45355,] "Paty" "Olga" "Adriana" "Mary" "Jonhatan" "Mario"
## [45356,] "Paty" "Olga" "Adriana" "Mary" "Mario" "Angel"
## [45357,] "Paty" "Olga" "Adriana" "Mary" "Mario" "Augusto"
## [45358,] "Paty" "Olga" "Adriana" "Mary" "Mario" "Daniel"
## [45359,] "Paty" "Olga" "Adriana" "Mary" "Mario" "Jesabel"
## [45360,] "Paty" "Olga" "Adriana" "Mary" "Mario" "Jonhatan"
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" "Angel" "Augusto" "Daniel" "Jesabel" "Paty"
## [2,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Paty"
## [3,] "Adriana" "Angel" "Augusto" "Daniel" "Mario" "Paty"
## [4,] "Adriana" "Angel" "Augusto" "Daniel" "Mary" "Paty"
## [5,] "Adriana" "Angel" "Augusto" "Daniel" "Olga" "Paty"
## [6,] "Adriana" "Angel" "Augusto" "Daniel" "Paty" "Jesabel"
tail(permutaciones[which(permutaciones[,4] == 'Paty' | permutaciones[,5] == 'Paty' | permutaciones[,6] == 'Paty'),])
## [,1] [,2] [,3] [,4] [,5] [,6]
## [45355,] "Olga" "Mary" "Mario" "Paty" "Jesabel" "Jonhatan"
## [45356,] "Olga" "Mary" "Mario" "Paty" "Jonhatan" "Adriana"
## [45357,] "Olga" "Mary" "Mario" "Paty" "Jonhatan" "Angel"
## [45358,] "Olga" "Mary" "Mario" "Paty" "Jonhatan" "Augusto"
## [45359,] "Olga" "Mary" "Mario" "Paty" "Jonhatan" "Daniel"
## [45360,] "Olga" "Mary" "Mario" "Paty" "Jonhatan" "Jesabel"
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" "Angel" "Augusto" "Daniel" "Jesabel" "Olga"
## [2,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Olga"
## [3,] "Adriana" "Angel" "Augusto" "Daniel" "Mario" "Olga"
## [4,] "Adriana" "Angel" "Augusto" "Daniel" "Mary" "Olga"
## [5,] "Adriana" "Angel" "Augusto" "Daniel" "Olga" "Jesabel"
## [6,] "Adriana" "Angel" "Augusto" "Daniel" "Olga" "Jonhatan"
tail(permutaciones[which(permutaciones[,4] == 'Olga' | permutaciones[,5] == 'Olga' | permutaciones[,6] == 'Olga'),])
## [,1] [,2] [,3] [,4] [,5] [,6]
## [45355,] "Paty" "Mary" "Mario" "Olga" "Jesabel" "Jonhatan"
## [45356,] "Paty" "Mary" "Mario" "Olga" "Jonhatan" "Adriana"
## [45357,] "Paty" "Mary" "Mario" "Olga" "Jonhatan" "Angel"
## [45358,] "Paty" "Mary" "Mario" "Olga" "Jonhatan" "Augusto"
## [45359,] "Paty" "Mary" "Mario" "Olga" "Jonhatan" "Daniel"
## [45360,] "Paty" "Mary" "Mario" "Olga" "Jonhatan" "Jesabel"
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" "Angel" "Augusto" "Daniel" "Jesabel" "Olga"
## [2,] "Adriana" "Angel" "Augusto" "Daniel" "Jonhatan" "Olga"
## [3,] "Adriana" "Angel" "Augusto" "Daniel" "Mario" "Olga"
## [4,] "Adriana" "Angel" "Augusto" "Daniel" "Mary" "Olga"
## [5,] "Adriana" "Angel" "Augusto" "Daniel" "Olga" "Jesabel"
## [6,] "Adriana" "Angel" "Augusto" "Daniel" "Olga" "Jonhatan"
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" "Mario" "Jesabel" "Jonhatan"
## [90716,] "Paty" "Olga" "Mary" "Mario" "Jonhatan" "Adriana"
## [90717,] "Paty" "Olga" "Mary" "Mario" "Jonhatan" "Angel"
## [90718,] "Paty" "Olga" "Mary" "Mario" "Jonhatan" "Augusto"
## [90719,] "Paty" "Olga" "Mary" "Mario" "Jonhatan" "Daniel"
## [90720,] "Paty" "Olga" "Mary" "Mario" "Jonhatan" "Jesabel"
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" "Angel" "Augusto" "Mary" "Olga" "Paty"
## [2,] "Adriana" "Angel" "Augusto" "Mary" "Paty" "Olga"
## [3,] "Adriana" "Angel" "Augusto" "Olga" "Mary" "Paty"
## [4,] "Adriana" "Angel" "Augusto" "Olga" "Paty" "Mary"
## [5,] "Adriana" "Angel" "Augusto" "Paty" "Mary" "Olga"
## [6,] "Adriana" "Angel" "Augusto" "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" "Mario" "Mary" "Adriana" "Jonhatan"
## [8996,] "Paty" "Olga" "Mario" "Mary" "Angel" "Adriana"
## [8997,] "Paty" "Olga" "Mario" "Mary" "Augusto" "Adriana"
## [8998,] "Paty" "Olga" "Mario" "Mary" "Daniel" "Adriana"
## [8999,] "Paty" "Olga" "Mario" "Mary" "Jesabel" "Adriana"
## [9000,] "Paty" "Olga" "Mario" "Mary" "Jonhatan" "Adriana"
20.- ¿En cuantas ocasiones de las PERMUTACIONES en grupos de SEIS se encuentra juntas “Adriana”, “Mary”, “Olga” y “Paty”?
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" "Angel" "Augusto"
## [2,] "Adriana" "Mary" "Olga" "Paty" "Angel" "Daniel"
## [3,] "Adriana" "Mary" "Olga" "Paty" "Angel" "Jesabel"
## [4,] "Adriana" "Mary" "Olga" "Paty" "Angel" "Jonhatan"
## [5,] "Adriana" "Mary" "Olga" "Paty" "Angel" "Mario"
## [6,] "Adriana" "Mary" "Olga" "Paty" "Augusto" "Angel"
## [7,] "Adriana" "Mary" "Olga" "Paty" "Augusto" "Daniel"
## [8,] "Adriana" "Mary" "Olga" "Paty" "Augusto" "Jesabel"
## [9,] "Adriana" "Mary" "Olga" "Paty" "Augusto" "Jonhatan"
## [10,] "Adriana" "Mary" "Olga" "Paty" "Augusto" "Mario"
## [11,] "Adriana" "Mary" "Olga" "Paty" "Daniel" "Angel"
## [12,] "Adriana" "Mary" "Olga" "Paty" "Daniel" "Augusto"
## [13,] "Adriana" "Mary" "Olga" "Paty" "Daniel" "Jesabel"
## [14,] "Adriana" "Mary" "Olga" "Paty" "Daniel" "Jonhatan"
## [15,] "Adriana" "Mary" "Olga" "Paty" "Daniel" "Mario"
## [16,] "Adriana" "Mary" "Olga" "Paty" "Jesabel" "Angel"
## [17,] "Adriana" "Mary" "Olga" "Paty" "Jesabel" "Augusto"
## [18,] "Adriana" "Mary" "Olga" "Paty" "Jesabel" "Daniel"
## [19,] "Adriana" "Mary" "Olga" "Paty" "Jesabel" "Jonhatan"
## [20,] "Adriana" "Mary" "Olga" "Paty" "Jesabel" "Mario"
## [21,] "Adriana" "Mary" "Olga" "Paty" "Jonhatan" "Angel"
## [22,] "Adriana" "Mary" "Olga" "Paty" "Jonhatan" "Augusto"
## [23,] "Adriana" "Mary" "Olga" "Paty" "Jonhatan" "Daniel"
## [24,] "Adriana" "Mary" "Olga" "Paty" "Jonhatan" "Jesabel"
## [25,] "Adriana" "Mary" "Olga" "Paty" "Jonhatan" "Mario"
## [26,] "Adriana" "Mary" "Olga" "Paty" "Mario" "Angel"
## [27,] "Adriana" "Mary" "Olga" "Paty" "Mario" "Augusto"
## [28,] "Adriana" "Mary" "Olga" "Paty" "Mario" "Daniel"
## [29,] "Adriana" "Mary" "Olga" "Paty" "Mario" "Jesabel"
## [30,] "Adriana" "Mary" "Olga" "Paty" "Mario" "Jonhatan"
## [31,] "Angel" "Adriana" "Mary" "Olga" "Paty" "Augusto"
## [32,] "Angel" "Adriana" "Mary" "Olga" "Paty" "Daniel"
## [33,] "Angel" "Adriana" "Mary" "Olga" "Paty" "Jesabel"
## [34,] "Angel" "Adriana" "Mary" "Olga" "Paty" "Jonhatan"
## [35,] "Angel" "Adriana" "Mary" "Olga" "Paty" "Mario"
## [36,] "Angel" "Augusto" "Adriana" "Mary" "Olga" "Paty"
## [37,] "Angel" "Daniel" "Adriana" "Mary" "Olga" "Paty"
## [38,] "Angel" "Jesabel" "Adriana" "Mary" "Olga" "Paty"
## [39,] "Angel" "Jonhatan" "Adriana" "Mary" "Olga" "Paty"
## [40,] "Angel" "Mario" "Adriana" "Mary" "Olga" "Paty"
## [41,] "Augusto" "Adriana" "Mary" "Olga" "Paty" "Angel"
## [42,] "Augusto" "Adriana" "Mary" "Olga" "Paty" "Daniel"
## [43,] "Augusto" "Adriana" "Mary" "Olga" "Paty" "Jesabel"
## [44,] "Augusto" "Adriana" "Mary" "Olga" "Paty" "Jonhatan"
## [45,] "Augusto" "Adriana" "Mary" "Olga" "Paty" "Mario"
## [46,] "Augusto" "Angel" "Adriana" "Mary" "Olga" "Paty"
## [47,] "Augusto" "Daniel" "Adriana" "Mary" "Olga" "Paty"
## [48,] "Augusto" "Jesabel" "Adriana" "Mary" "Olga" "Paty"
## [49,] "Augusto" "Jonhatan" "Adriana" "Mary" "Olga" "Paty"
## [50,] "Augusto" "Mario" "Adriana" "Mary" "Olga" "Paty"
## [51,] "Daniel" "Adriana" "Mary" "Olga" "Paty" "Angel"
## [52,] "Daniel" "Adriana" "Mary" "Olga" "Paty" "Augusto"
## [53,] "Daniel" "Adriana" "Mary" "Olga" "Paty" "Jesabel"
## [54,] "Daniel" "Adriana" "Mary" "Olga" "Paty" "Jonhatan"
## [55,] "Daniel" "Adriana" "Mary" "Olga" "Paty" "Mario"
## [56,] "Daniel" "Angel" "Adriana" "Mary" "Olga" "Paty"
## [57,] "Daniel" "Augusto" "Adriana" "Mary" "Olga" "Paty"
## [58,] "Daniel" "Jesabel" "Adriana" "Mary" "Olga" "Paty"
## [59,] "Daniel" "Jonhatan" "Adriana" "Mary" "Olga" "Paty"
## [60,] "Daniel" "Mario" "Adriana" "Mary" "Olga" "Paty"
## [61,] "Jesabel" "Adriana" "Mary" "Olga" "Paty" "Angel"
## [62,] "Jesabel" "Adriana" "Mary" "Olga" "Paty" "Augusto"
## [63,] "Jesabel" "Adriana" "Mary" "Olga" "Paty" "Daniel"
## [64,] "Jesabel" "Adriana" "Mary" "Olga" "Paty" "Jonhatan"
## [65,] "Jesabel" "Adriana" "Mary" "Olga" "Paty" "Mario"
## [66,] "Jesabel" "Angel" "Adriana" "Mary" "Olga" "Paty"
## [67,] "Jesabel" "Augusto" "Adriana" "Mary" "Olga" "Paty"
## [68,] "Jesabel" "Daniel" "Adriana" "Mary" "Olga" "Paty"
## [69,] "Jesabel" "Jonhatan" "Adriana" "Mary" "Olga" "Paty"
## [70,] "Jesabel" "Mario" "Adriana" "Mary" "Olga" "Paty"
## [71,] "Jonhatan" "Adriana" "Mary" "Olga" "Paty" "Angel"
## [72,] "Jonhatan" "Adriana" "Mary" "Olga" "Paty" "Augusto"
## [73,] "Jonhatan" "Adriana" "Mary" "Olga" "Paty" "Daniel"
## [74,] "Jonhatan" "Adriana" "Mary" "Olga" "Paty" "Jesabel"
## [75,] "Jonhatan" "Adriana" "Mary" "Olga" "Paty" "Mario"
## [76,] "Jonhatan" "Angel" "Adriana" "Mary" "Olga" "Paty"
## [77,] "Jonhatan" "Augusto" "Adriana" "Mary" "Olga" "Paty"
## [78,] "Jonhatan" "Daniel" "Adriana" "Mary" "Olga" "Paty"
## [79,] "Jonhatan" "Jesabel" "Adriana" "Mary" "Olga" "Paty"
## [80,] "Jonhatan" "Mario" "Adriana" "Mary" "Olga" "Paty"
## [81,] "Mario" "Adriana" "Mary" "Olga" "Paty" "Angel"
## [82,] "Mario" "Adriana" "Mary" "Olga" "Paty" "Augusto"
## [83,] "Mario" "Adriana" "Mary" "Olga" "Paty" "Daniel"
## [84,] "Mario" "Adriana" "Mary" "Olga" "Paty" "Jesabel"
## [85,] "Mario" "Adriana" "Mary" "Olga" "Paty" "Jonhatan"
## [86,] "Mario" "Angel" "Adriana" "Mary" "Olga" "Paty"
## [87,] "Mario" "Augusto" "Adriana" "Mary" "Olga" "Paty"
## [88,] "Mario" "Daniel" "Adriana" "Mary" "Olga" "Paty"
## [89,] "Mario" "Jesabel" "Adriana" "Mary" "Olga" "Paty"
## [90,] "Mario" "Jonhatan" "Adriana" "Mary" "Olga" "Paty"