Hacer Combinaciones y Permutaciones
Por medio de funcioens de combinations() y permutations() simular combinaciones y permutaciones.
# install.packages("gtools")
library(gtools)Hacer combinaciones de nombres de personas
nombres <- c("JUAN", "JESUS", "PEDRO", "MARY", "LUCY", "ARACELY", "ZENAIDA")
nombres## [1] "JUAN" "JESUS" "PEDRO" "MARY" "LUCY" "ARACELY" "ZENAIDA"n <- length(nombres)\[ S=Cn\binom{n}{r} = \frac{n!}{(r!(n-r)!)} \]
r <- 2
C <- factorial(n) / (factorial(r) * factorial(n-r))
C## [1] 21combinar <- combinations(n = n, r = r, v = nombres)
combinar## [,1] [,2]
## [1,] "ARACELY" "JESUS"
## [2,] "ARACELY" "JUAN"
## [3,] "ARACELY" "LUCY"
## [4,] "ARACELY" "MARY"
## [5,] "ARACELY" "PEDRO"
## [6,] "ARACELY" "ZENAIDA"
## [7,] "JESUS" "JUAN"
## [8,] "JESUS" "LUCY"
## [9,] "JESUS" "MARY"
## [10,] "JESUS" "PEDRO"
## [11,] "JESUS" "ZENAIDA"
## [12,] "JUAN" "LUCY"
## [13,] "JUAN" "MARY"
## [14,] "JUAN" "PEDRO"
## [15,] "JUAN" "ZENAIDA"
## [16,] "LUCY" "MARY"
## [17,] "LUCY" "PEDRO"
## [18,] "LUCY" "ZENAIDA"
## [19,] "MARY" "PEDRO"
## [20,] "MARY" "ZENAIDA"
## [21,] "PEDRO" "ZENAIDA"r <- 3
C <- factorial(n) / (factorial(r) * factorial(n-r))
C## [1] 35Hacer combinaciones en grupos de 3 en 3
combinar <- combinations(n = n, r = r, v = nombres)
combinar## [,1] [,2] [,3]
## [1,] "ARACELY" "JESUS" "JUAN"
## [2,] "ARACELY" "JESUS" "LUCY"
## [3,] "ARACELY" "JESUS" "MARY"
## [4,] "ARACELY" "JESUS" "PEDRO"
## [5,] "ARACELY" "JESUS" "ZENAIDA"
## [6,] "ARACELY" "JUAN" "LUCY"
## [7,] "ARACELY" "JUAN" "MARY"
## [8,] "ARACELY" "JUAN" "PEDRO"
## [9,] "ARACELY" "JUAN" "ZENAIDA"
## [10,] "ARACELY" "LUCY" "MARY"
## [11,] "ARACELY" "LUCY" "PEDRO"
## [12,] "ARACELY" "LUCY" "ZENAIDA"
## [13,] "ARACELY" "MARY" "PEDRO"
## [14,] "ARACELY" "MARY" "ZENAIDA"
## [15,] "ARACELY" "PEDRO" "ZENAIDA"
## [16,] "JESUS" "JUAN" "LUCY"
## [17,] "JESUS" "JUAN" "MARY"
## [18,] "JESUS" "JUAN" "PEDRO"
## [19,] "JESUS" "JUAN" "ZENAIDA"
## [20,] "JESUS" "LUCY" "MARY"
## [21,] "JESUS" "LUCY" "PEDRO"
## [22,] "JESUS" "LUCY" "ZENAIDA"
## [23,] "JESUS" "MARY" "PEDRO"
## [24,] "JESUS" "MARY" "ZENAIDA"
## [25,] "JESUS" "PEDRO" "ZENAIDA"
## [26,] "JUAN" "LUCY" "MARY"
## [27,] "JUAN" "LUCY" "PEDRO"
## [28,] "JUAN" "LUCY" "ZENAIDA"
## [29,] "JUAN" "MARY" "PEDRO"
## [30,] "JUAN" "MARY" "ZENAIDA"
## [31,] "JUAN" "PEDRO" "ZENAIDA"
## [32,] "LUCY" "MARY" "PEDRO"
## [33,] "LUCY" "MARY" "ZENAIDA"
## [34,] "LUCY" "PEDRO" "ZENAIDA"
## [35,] "MARY" "PEDRO" "ZENAIDA"El orden de los elementos SI importa
\[ S = Pr\binom{n}{r} = \frac{n!}{(n-r)!} \]
r <- 2
P <- factorial(n) / factorial(n-r)
P## [1] 42permutar <- permutations(n = n, r = r, v = nombres)
permutar## [,1] [,2]
## [1,] "ARACELY" "JESUS"
## [2,] "ARACELY" "JUAN"
## [3,] "ARACELY" "LUCY"
## [4,] "ARACELY" "MARY"
## [5,] "ARACELY" "PEDRO"
## [6,] "ARACELY" "ZENAIDA"
## [7,] "JESUS" "ARACELY"
## [8,] "JESUS" "JUAN"
## [9,] "JESUS" "LUCY"
## [10,] "JESUS" "MARY"
## [11,] "JESUS" "PEDRO"
## [12,] "JESUS" "ZENAIDA"
## [13,] "JUAN" "ARACELY"
## [14,] "JUAN" "JESUS"
## [15,] "JUAN" "LUCY"
## [16,] "JUAN" "MARY"
## [17,] "JUAN" "PEDRO"
## [18,] "JUAN" "ZENAIDA"
## [19,] "LUCY" "ARACELY"
## [20,] "LUCY" "JESUS"
## [21,] "LUCY" "JUAN"
## [22,] "LUCY" "MARY"
## [23,] "LUCY" "PEDRO"
## [24,] "LUCY" "ZENAIDA"
## [25,] "MARY" "ARACELY"
## [26,] "MARY" "JESUS"
## [27,] "MARY" "JUAN"
## [28,] "MARY" "LUCY"
## [29,] "MARY" "PEDRO"
## [30,] "MARY" "ZENAIDA"
## [31,] "PEDRO" "ARACELY"
## [32,] "PEDRO" "JESUS"
## [33,] "PEDRO" "JUAN"
## [34,] "PEDRO" "LUCY"
## [35,] "PEDRO" "MARY"
## [36,] "PEDRO" "ZENAIDA"
## [37,] "ZENAIDA" "ARACELY"
## [38,] "ZENAIDA" "JESUS"
## [39,] "ZENAIDA" "JUAN"
## [40,] "ZENAIDA" "LUCY"
## [41,] "ZENAIDA" "MARY"
## [42,] "ZENAIDA" "PEDRO"r <- 3
P <- factorial(n) / factorial(n-r)
P## [1] 210permutar <- permutations(n = n, r = r, v = nombres)
permutar## [,1] [,2] [,3]
## [1,] "ARACELY" "JESUS" "JUAN"
## [2,] "ARACELY" "JESUS" "LUCY"
## [3,] "ARACELY" "JESUS" "MARY"
## [4,] "ARACELY" "JESUS" "PEDRO"
## [5,] "ARACELY" "JESUS" "ZENAIDA"
## [6,] "ARACELY" "JUAN" "JESUS"
## [7,] "ARACELY" "JUAN" "LUCY"
## [8,] "ARACELY" "JUAN" "MARY"
## [9,] "ARACELY" "JUAN" "PEDRO"
## [10,] "ARACELY" "JUAN" "ZENAIDA"
## [11,] "ARACELY" "LUCY" "JESUS"
## [12,] "ARACELY" "LUCY" "JUAN"
## [13,] "ARACELY" "LUCY" "MARY"
## [14,] "ARACELY" "LUCY" "PEDRO"
## [15,] "ARACELY" "LUCY" "ZENAIDA"
## [16,] "ARACELY" "MARY" "JESUS"
## [17,] "ARACELY" "MARY" "JUAN"
## [18,] "ARACELY" "MARY" "LUCY"
## [19,] "ARACELY" "MARY" "PEDRO"
## [20,] "ARACELY" "MARY" "ZENAIDA"
## [21,] "ARACELY" "PEDRO" "JESUS"
## [22,] "ARACELY" "PEDRO" "JUAN"
## [23,] "ARACELY" "PEDRO" "LUCY"
## [24,] "ARACELY" "PEDRO" "MARY"
## [25,] "ARACELY" "PEDRO" "ZENAIDA"
## [26,] "ARACELY" "ZENAIDA" "JESUS"
## [27,] "ARACELY" "ZENAIDA" "JUAN"
## [28,] "ARACELY" "ZENAIDA" "LUCY"
## [29,] "ARACELY" "ZENAIDA" "MARY"
## [30,] "ARACELY" "ZENAIDA" "PEDRO"
## [31,] "JESUS" "ARACELY" "JUAN"
## [32,] "JESUS" "ARACELY" "LUCY"
## [33,] "JESUS" "ARACELY" "MARY"
## [34,] "JESUS" "ARACELY" "PEDRO"
## [35,] "JESUS" "ARACELY" "ZENAIDA"
## [36,] "JESUS" "JUAN" "ARACELY"
## [37,] "JESUS" "JUAN" "LUCY"
## [38,] "JESUS" "JUAN" "MARY"
## [39,] "JESUS" "JUAN" "PEDRO"
## [40,] "JESUS" "JUAN" "ZENAIDA"
## [41,] "JESUS" "LUCY" "ARACELY"
## [42,] "JESUS" "LUCY" "JUAN"
## [43,] "JESUS" "LUCY" "MARY"
## [44,] "JESUS" "LUCY" "PEDRO"
## [45,] "JESUS" "LUCY" "ZENAIDA"
## [46,] "JESUS" "MARY" "ARACELY"
## [47,] "JESUS" "MARY" "JUAN"
## [48,] "JESUS" "MARY" "LUCY"
## [49,] "JESUS" "MARY" "PEDRO"
## [50,] "JESUS" "MARY" "ZENAIDA"
## [51,] "JESUS" "PEDRO" "ARACELY"
## [52,] "JESUS" "PEDRO" "JUAN"
## [53,] "JESUS" "PEDRO" "LUCY"
## [54,] "JESUS" "PEDRO" "MARY"
## [55,] "JESUS" "PEDRO" "ZENAIDA"
## [56,] "JESUS" "ZENAIDA" "ARACELY"
## [57,] "JESUS" "ZENAIDA" "JUAN"
## [58,] "JESUS" "ZENAIDA" "LUCY"
## [59,] "JESUS" "ZENAIDA" "MARY"
## [60,] "JESUS" "ZENAIDA" "PEDRO"
## [61,] "JUAN" "ARACELY" "JESUS"
## [62,] "JUAN" "ARACELY" "LUCY"
## [63,] "JUAN" "ARACELY" "MARY"
## [64,] "JUAN" "ARACELY" "PEDRO"
## [65,] "JUAN" "ARACELY" "ZENAIDA"
## [66,] "JUAN" "JESUS" "ARACELY"
## [67,] "JUAN" "JESUS" "LUCY"
## [68,] "JUAN" "JESUS" "MARY"
## [69,] "JUAN" "JESUS" "PEDRO"
## [70,] "JUAN" "JESUS" "ZENAIDA"
## [71,] "JUAN" "LUCY" "ARACELY"
## [72,] "JUAN" "LUCY" "JESUS"
## [73,] "JUAN" "LUCY" "MARY"
## [74,] "JUAN" "LUCY" "PEDRO"
## [75,] "JUAN" "LUCY" "ZENAIDA"
## [76,] "JUAN" "MARY" "ARACELY"
## [77,] "JUAN" "MARY" "JESUS"
## [78,] "JUAN" "MARY" "LUCY"
## [79,] "JUAN" "MARY" "PEDRO"
## [80,] "JUAN" "MARY" "ZENAIDA"
## [81,] "JUAN" "PEDRO" "ARACELY"
## [82,] "JUAN" "PEDRO" "JESUS"
## [83,] "JUAN" "PEDRO" "LUCY"
## [84,] "JUAN" "PEDRO" "MARY"
## [85,] "JUAN" "PEDRO" "ZENAIDA"
## [86,] "JUAN" "ZENAIDA" "ARACELY"
## [87,] "JUAN" "ZENAIDA" "JESUS"
## [88,] "JUAN" "ZENAIDA" "LUCY"
## [89,] "JUAN" "ZENAIDA" "MARY"
## [90,] "JUAN" "ZENAIDA" "PEDRO"
## [91,] "LUCY" "ARACELY" "JESUS"
## [92,] "LUCY" "ARACELY" "JUAN"
## [93,] "LUCY" "ARACELY" "MARY"
## [94,] "LUCY" "ARACELY" "PEDRO"
## [95,] "LUCY" "ARACELY" "ZENAIDA"
## [96,] "LUCY" "JESUS" "ARACELY"
## [97,] "LUCY" "JESUS" "JUAN"
## [98,] "LUCY" "JESUS" "MARY"
## [99,] "LUCY" "JESUS" "PEDRO"
## [100,] "LUCY" "JESUS" "ZENAIDA"
## [101,] "LUCY" "JUAN" "ARACELY"
## [102,] "LUCY" "JUAN" "JESUS"
## [103,] "LUCY" "JUAN" "MARY"
## [104,] "LUCY" "JUAN" "PEDRO"
## [105,] "LUCY" "JUAN" "ZENAIDA"
## [106,] "LUCY" "MARY" "ARACELY"
## [107,] "LUCY" "MARY" "JESUS"
## [108,] "LUCY" "MARY" "JUAN"
## [109,] "LUCY" "MARY" "PEDRO"
## [110,] "LUCY" "MARY" "ZENAIDA"
## [111,] "LUCY" "PEDRO" "ARACELY"
## [112,] "LUCY" "PEDRO" "JESUS"
## [113,] "LUCY" "PEDRO" "JUAN"
## [114,] "LUCY" "PEDRO" "MARY"
## [115,] "LUCY" "PEDRO" "ZENAIDA"
## [116,] "LUCY" "ZENAIDA" "ARACELY"
## [117,] "LUCY" "ZENAIDA" "JESUS"
## [118,] "LUCY" "ZENAIDA" "JUAN"
## [119,] "LUCY" "ZENAIDA" "MARY"
## [120,] "LUCY" "ZENAIDA" "PEDRO"
## [121,] "MARY" "ARACELY" "JESUS"
## [122,] "MARY" "ARACELY" "JUAN"
## [123,] "MARY" "ARACELY" "LUCY"
## [124,] "MARY" "ARACELY" "PEDRO"
## [125,] "MARY" "ARACELY" "ZENAIDA"
## [126,] "MARY" "JESUS" "ARACELY"
## [127,] "MARY" "JESUS" "JUAN"
## [128,] "MARY" "JESUS" "LUCY"
## [129,] "MARY" "JESUS" "PEDRO"
## [130,] "MARY" "JESUS" "ZENAIDA"
## [131,] "MARY" "JUAN" "ARACELY"
## [132,] "MARY" "JUAN" "JESUS"
## [133,] "MARY" "JUAN" "LUCY"
## [134,] "MARY" "JUAN" "PEDRO"
## [135,] "MARY" "JUAN" "ZENAIDA"
## [136,] "MARY" "LUCY" "ARACELY"
## [137,] "MARY" "LUCY" "JESUS"
## [138,] "MARY" "LUCY" "JUAN"
## [139,] "MARY" "LUCY" "PEDRO"
## [140,] "MARY" "LUCY" "ZENAIDA"
## [141,] "MARY" "PEDRO" "ARACELY"
## [142,] "MARY" "PEDRO" "JESUS"
## [143,] "MARY" "PEDRO" "JUAN"
## [144,] "MARY" "PEDRO" "LUCY"
## [145,] "MARY" "PEDRO" "ZENAIDA"
## [146,] "MARY" "ZENAIDA" "ARACELY"
## [147,] "MARY" "ZENAIDA" "JESUS"
## [148,] "MARY" "ZENAIDA" "JUAN"
## [149,] "MARY" "ZENAIDA" "LUCY"
## [150,] "MARY" "ZENAIDA" "PEDRO"
## [151,] "PEDRO" "ARACELY" "JESUS"
## [152,] "PEDRO" "ARACELY" "JUAN"
## [153,] "PEDRO" "ARACELY" "LUCY"
## [154,] "PEDRO" "ARACELY" "MARY"
## [155,] "PEDRO" "ARACELY" "ZENAIDA"
## [156,] "PEDRO" "JESUS" "ARACELY"
## [157,] "PEDRO" "JESUS" "JUAN"
## [158,] "PEDRO" "JESUS" "LUCY"
## [159,] "PEDRO" "JESUS" "MARY"
## [160,] "PEDRO" "JESUS" "ZENAIDA"
## [161,] "PEDRO" "JUAN" "ARACELY"
## [162,] "PEDRO" "JUAN" "JESUS"
## [163,] "PEDRO" "JUAN" "LUCY"
## [164,] "PEDRO" "JUAN" "MARY"
## [165,] "PEDRO" "JUAN" "ZENAIDA"
## [166,] "PEDRO" "LUCY" "ARACELY"
## [167,] "PEDRO" "LUCY" "JESUS"
## [168,] "PEDRO" "LUCY" "JUAN"
## [169,] "PEDRO" "LUCY" "MARY"
## [170,] "PEDRO" "LUCY" "ZENAIDA"
## [171,] "PEDRO" "MARY" "ARACELY"
## [172,] "PEDRO" "MARY" "JESUS"
## [173,] "PEDRO" "MARY" "JUAN"
## [174,] "PEDRO" "MARY" "LUCY"
## [175,] "PEDRO" "MARY" "ZENAIDA"
## [176,] "PEDRO" "ZENAIDA" "ARACELY"
## [177,] "PEDRO" "ZENAIDA" "JESUS"
## [178,] "PEDRO" "ZENAIDA" "JUAN"
## [179,] "PEDRO" "ZENAIDA" "LUCY"
## [180,] "PEDRO" "ZENAIDA" "MARY"
## [181,] "ZENAIDA" "ARACELY" "JESUS"
## [182,] "ZENAIDA" "ARACELY" "JUAN"
## [183,] "ZENAIDA" "ARACELY" "LUCY"
## [184,] "ZENAIDA" "ARACELY" "MARY"
## [185,] "ZENAIDA" "ARACELY" "PEDRO"
## [186,] "ZENAIDA" "JESUS" "ARACELY"
## [187,] "ZENAIDA" "JESUS" "JUAN"
## [188,] "ZENAIDA" "JESUS" "LUCY"
## [189,] "ZENAIDA" "JESUS" "MARY"
## [190,] "ZENAIDA" "JESUS" "PEDRO"
## [191,] "ZENAIDA" "JUAN" "ARACELY"
## [192,] "ZENAIDA" "JUAN" "JESUS"
## [193,] "ZENAIDA" "JUAN" "LUCY"
## [194,] "ZENAIDA" "JUAN" "MARY"
## [195,] "ZENAIDA" "JUAN" "PEDRO"
## [196,] "ZENAIDA" "LUCY" "ARACELY"
## [197,] "ZENAIDA" "LUCY" "JESUS"
## [198,] "ZENAIDA" "LUCY" "JUAN"
## [199,] "ZENAIDA" "LUCY" "MARY"
## [200,] "ZENAIDA" "LUCY" "PEDRO"
## [201,] "ZENAIDA" "MARY" "ARACELY"
## [202,] "ZENAIDA" "MARY" "JESUS"
## [203,] "ZENAIDA" "MARY" "JUAN"
## [204,] "ZENAIDA" "MARY" "LUCY"
## [205,] "ZENAIDA" "MARY" "PEDRO"
## [206,] "ZENAIDA" "PEDRO" "ARACELY"
## [207,] "ZENAIDA" "PEDRO" "JESUS"
## [208,] "ZENAIDA" "PEDRO" "JUAN"
## [209,] "ZENAIDA" "PEDRO" "LUCY"
## [210,] "ZENAIDA" "PEDRO" "MARY"Las combinaciones y permutaciones sirven para formar espacios muestrales que permitan encontrar o visualizar probabilidades de acuerdo a tareas específica.