Caso 07 Factorial y Combinaciones
Marco Antonio Mauricio Martínez
2023-02-26
1 Objetivo
Construir combinaciones de conjuntos de datos de personas y de nombres de equipos deportivos.
2 Descripción
A partir de conjuntos datos (valores individuales) realizar combinaciones para conocer el número de las mismas y el acomodo de los valores para su interpretación en términos de probabilidad.
Cargar librerías
Cargar los datos
Identificar fórmula de factorial
Identificar fórmula de combinaciones
Determinar probabilidades a partir del espacio muestral de las combinaciones
Encontrar probabilidad con base en frecuencia o contabilizar eventos específicos del espacio muestral
Interpretar el caso
2.1 Cargar librerías
Se van a utilizar funciones de la librería “gtools” por lo que se necesario instalarla previamente: install.packages(“gtools”).
Esta librería permitirá hacer combinaciones y permutaciones.
# install.packages("gtools")
library(gtools)3 Marco conceptual
Para hacer combinaciones es necesario identificar la importancia del valor factorial de un número
3.1 Factorial
El factorial de un número es el producto de \(n\) por todos los naturales menores que el y se representa con el \(!n\), entonces \(n!=n\times(n-1)...\times 1\).
La notación ! significa factorial; por ejemplo, 5 factorial es 5! = (5)(4)(3)(2)(1) = 120. (Anderson, Sweeney, and Williams 2008) .
La función factorial es una fórmula matemática representada por el signo de exclamación \(!\). En la fórmula Factorial se deben multiplicar todos los números enteros y positivos que hay entre el número que aparece en la fórmula y el número \(1\). (Walpole, Myers, and Myers 2012).
Ejemplo: hallar el factorial de 6 o se sea \(6!=6\times5\times4\times3\times2\times1=720\)
3.2 Combinaciones
La regla de conteo de combinaciones permite contar el número de resultados experimentales cuando el experimento consiste en \(r\) objetos de un conjunto (usualmente mayor) de \(n\) objetos.
El número de combinaciones distintas de \(n\) objetos distintos que se pueden formar, tomando \(r\) de ellos a un tiempo. (Mendenhall, Beaver, and Beaver 2010).
3.2.1 Fórmula de combinaciones
\[ S=Cn\binom{n}{r} = \frac{n!}{(r!\cdot(n-r)!)}\\S \text{ es el espacio muestral y la cantidad de combinaciones} \\Cn \text{ es el número de combinaciones posibles}\\ \binom{n}{r} \text {es símbolo de combinar n elementos en grupos de r}\\ n \text{ es el total de elementos}\\ r \text{ es de cuantos en cuantos elementos se hacen grupos} \]
3.3 Ejemplo 1. Nombres de personas
Se trata de hacer combinaciones con los nombres de cuatro personas: “Oscar”, “Paco”, “Paty”, “Laura” … … (otros nombres) en grupos de 2. Entonces \(n=4\), porque hay cuatro nombres o elementos y \(r=2\) porque se trata de agrupar de dos en dos.
¿Cuántas combinaciones deberá haber?
Oscar y Paco
Oscar y Paty
Oscar y Laura
Paco y Paty
… …
Paty y Laura
nombres <- c("Oscar", "Paco", "Paty", "Laura", "Rubén", "Andrés", "Lucy", "Alberto", "Juan", "Yariel", "Sebastián", "Fani", "Emilio", "Yareli")
n <- length(nombres)
r <- 2 # ¿cómo agrupar?
Cn <- factorial(n) / (factorial(r) * factorial(n-r))
paste("Existen ", Cn , " posibles combinaciones del total de ", n , " nombres ", " en grupos de ", r ," en ", r)## [1] "Existen 91 posibles combinaciones del total de 14 nombres en grupos de 2 en 2"3.4 Ejemplo 2. Nombres de compañías.
Se trata de hacer combinaciones con los nombres de diez compañías: “Blizzard”, “Activision”, “Nintendo”, “Konami”, “2K Games”, “Ubisoft”, “EA”, “Square Enix”, “Moon Studios”, “From Software” en grupos de 5. Entonces \(n=9\), porque hay diez compañías o elementos y \(r=5\) porque se trata de agrupar de cinco en cinco.
¿Cuántas combinaciones deberá haber?
empresas = c("Blizzard", "Activision", "Nintendo", "Konami", "2K Games", "Ubisoft", "EA", "Square Enix", "Moon Studios", "From Software")
n <- length(empresas)
r <- 5 # ¿cómo agrupar?
Cn <- factorial(n) / (factorial(r) * factorial(n-r))
paste("Existen", Cn , "posibles combinaciones del total de", n , "compañías", "en grupos de", r ,"en", r)## [1] "Existen 252 posibles combinaciones del total de 10 compañías en grupos de 5 en 5"4 Desarrollo
Hacer combinaciones con nombres de personas
Si bien la fórmula de combinaciones indica el número de combinaciones posibles de un conjunto de elementos pero lo que se desea conocer es ¿cómo se forman las combinaciones o cómo se verían los grupos formados?.
Se utiliza la función combination().
4.1 Combinaciones de nombres
Se utiliza la función combinations() y se requiere por lo menos tres atributos:
La cantidad de elementos n
Los grupos de cuanto en cuanto se forman r
y los elementos, o sea en este caso el vector v
4.1.1 Nombres de personas
Se muestran las posibles combinaciones de los nombres de personas. Las función combinations() ordena los valores alfabéticamente y luego construye las combinaciones.
nombres## [1] "Oscar" "Paco" "Paty" "Laura" "Rubén" "Andrés"
## [7] "Lucy" "Alberto" "Juan" "Yariel" "Sebastián" "Fani"
## [13] "Emilio" "Yareli"Cn.nombres <- combinations(n = length(nombres), r = 2, v = nombres)
Cn.nombres## [,1] [,2]
## [1,] "Alberto" "Andrés"
## [2,] "Alberto" "Emilio"
## [3,] "Alberto" "Fani"
## [4,] "Alberto" "Juan"
## [5,] "Alberto" "Laura"
## [6,] "Alberto" "Lucy"
## [7,] "Alberto" "Oscar"
## [8,] "Alberto" "Paco"
## [9,] "Alberto" "Paty"
## [10,] "Alberto" "Rubén"
## [11,] "Alberto" "Sebastián"
## [12,] "Alberto" "Yareli"
## [13,] "Alberto" "Yariel"
## [14,] "Andrés" "Emilio"
## [15,] "Andrés" "Fani"
## [16,] "Andrés" "Juan"
## [17,] "Andrés" "Laura"
## [18,] "Andrés" "Lucy"
## [19,] "Andrés" "Oscar"
## [20,] "Andrés" "Paco"
## [21,] "Andrés" "Paty"
## [22,] "Andrés" "Rubén"
## [23,] "Andrés" "Sebastián"
## [24,] "Andrés" "Yareli"
## [25,] "Andrés" "Yariel"
## [26,] "Emilio" "Fani"
## [27,] "Emilio" "Juan"
## [28,] "Emilio" "Laura"
## [29,] "Emilio" "Lucy"
## [30,] "Emilio" "Oscar"
## [31,] "Emilio" "Paco"
## [32,] "Emilio" "Paty"
## [33,] "Emilio" "Rubén"
## [34,] "Emilio" "Sebastián"
## [35,] "Emilio" "Yareli"
## [36,] "Emilio" "Yariel"
## [37,] "Fani" "Juan"
## [38,] "Fani" "Laura"
## [39,] "Fani" "Lucy"
## [40,] "Fani" "Oscar"
## [41,] "Fani" "Paco"
## [42,] "Fani" "Paty"
## [43,] "Fani" "Rubén"
## [44,] "Fani" "Sebastián"
## [45,] "Fani" "Yareli"
## [46,] "Fani" "Yariel"
## [47,] "Juan" "Laura"
## [48,] "Juan" "Lucy"
## [49,] "Juan" "Oscar"
## [50,] "Juan" "Paco"
## [51,] "Juan" "Paty"
## [52,] "Juan" "Rubén"
## [53,] "Juan" "Sebastián"
## [54,] "Juan" "Yareli"
## [55,] "Juan" "Yariel"
## [56,] "Laura" "Lucy"
## [57,] "Laura" "Oscar"
## [58,] "Laura" "Paco"
## [59,] "Laura" "Paty"
## [60,] "Laura" "Rubén"
## [61,] "Laura" "Sebastián"
## [62,] "Laura" "Yareli"
## [63,] "Laura" "Yariel"
## [64,] "Lucy" "Oscar"
## [65,] "Lucy" "Paco"
## [66,] "Lucy" "Paty"
## [67,] "Lucy" "Rubén"
## [68,] "Lucy" "Sebastián"
## [69,] "Lucy" "Yareli"
## [70,] "Lucy" "Yariel"
## [71,] "Oscar" "Paco"
## [72,] "Oscar" "Paty"
## [73,] "Oscar" "Rubén"
## [74,] "Oscar" "Sebastián"
## [75,] "Oscar" "Yareli"
## [76,] "Oscar" "Yariel"
## [77,] "Paco" "Paty"
## [78,] "Paco" "Rubén"
## [79,] "Paco" "Sebastián"
## [80,] "Paco" "Yareli"
## [81,] "Paco" "Yariel"
## [82,] "Paty" "Rubén"
## [83,] "Paty" "Sebastián"
## [84,] "Paty" "Yareli"
## [85,] "Paty" "Yariel"
## [86,] "Rubén" "Sebastián"
## [87,] "Rubén" "Yareli"
## [88,] "Rubén" "Yariel"
## [89,] "Sebastián" "Yareli"
## [90,] "Sebastián" "Yariel"
## [91,] "Yareli" "Yariel"4.1.2 Nombres de compañías
Se muestran las posibles combinaciones de los nombres de compañías.
empresas## [1] "Blizzard" "Activision" "Nintendo" "Konami"
## [5] "2K Games" "Ubisoft" "EA" "Square Enix"
## [9] "Moon Studios" "From Software"Cn.empresas = combinations(n = length(empresas), r = 5, v = empresas)
Cn.empresas## [,1] [,2] [,3] [,4]
## [1,] "2K Games" "Activision" "Blizzard" "EA"
## [2,] "2K Games" "Activision" "Blizzard" "EA"
## [3,] "2K Games" "Activision" "Blizzard" "EA"
## [4,] "2K Games" "Activision" "Blizzard" "EA"
## [5,] "2K Games" "Activision" "Blizzard" "EA"
## [6,] "2K Games" "Activision" "Blizzard" "EA"
## [7,] "2K Games" "Activision" "Blizzard" "From Software"
## [8,] "2K Games" "Activision" "Blizzard" "From Software"
## [9,] "2K Games" "Activision" "Blizzard" "From Software"
## [10,] "2K Games" "Activision" "Blizzard" "From Software"
## [11,] "2K Games" "Activision" "Blizzard" "From Software"
## [12,] "2K Games" "Activision" "Blizzard" "Konami"
## [13,] "2K Games" "Activision" "Blizzard" "Konami"
## [14,] "2K Games" "Activision" "Blizzard" "Konami"
## [15,] "2K Games" "Activision" "Blizzard" "Konami"
## [16,] "2K Games" "Activision" "Blizzard" "Moon Studios"
## [17,] "2K Games" "Activision" "Blizzard" "Moon Studios"
## [18,] "2K Games" "Activision" "Blizzard" "Moon Studios"
## [19,] "2K Games" "Activision" "Blizzard" "Nintendo"
## [20,] "2K Games" "Activision" "Blizzard" "Nintendo"
## [21,] "2K Games" "Activision" "Blizzard" "Square Enix"
## [22,] "2K Games" "Activision" "EA" "From Software"
## [23,] "2K Games" "Activision" "EA" "From Software"
## [24,] "2K Games" "Activision" "EA" "From Software"
## [25,] "2K Games" "Activision" "EA" "From Software"
## [26,] "2K Games" "Activision" "EA" "From Software"
## [27,] "2K Games" "Activision" "EA" "Konami"
## [28,] "2K Games" "Activision" "EA" "Konami"
## [29,] "2K Games" "Activision" "EA" "Konami"
## [30,] "2K Games" "Activision" "EA" "Konami"
## [31,] "2K Games" "Activision" "EA" "Moon Studios"
## [32,] "2K Games" "Activision" "EA" "Moon Studios"
## [33,] "2K Games" "Activision" "EA" "Moon Studios"
## [34,] "2K Games" "Activision" "EA" "Nintendo"
## [35,] "2K Games" "Activision" "EA" "Nintendo"
## [36,] "2K Games" "Activision" "EA" "Square Enix"
## [37,] "2K Games" "Activision" "From Software" "Konami"
## [38,] "2K Games" "Activision" "From Software" "Konami"
## [39,] "2K Games" "Activision" "From Software" "Konami"
## [40,] "2K Games" "Activision" "From Software" "Konami"
## [41,] "2K Games" "Activision" "From Software" "Moon Studios"
## [42,] "2K Games" "Activision" "From Software" "Moon Studios"
## [43,] "2K Games" "Activision" "From Software" "Moon Studios"
## [44,] "2K Games" "Activision" "From Software" "Nintendo"
## [45,] "2K Games" "Activision" "From Software" "Nintendo"
## [46,] "2K Games" "Activision" "From Software" "Square Enix"
## [47,] "2K Games" "Activision" "Konami" "Moon Studios"
## [48,] "2K Games" "Activision" "Konami" "Moon Studios"
## [49,] "2K Games" "Activision" "Konami" "Moon Studios"
## [50,] "2K Games" "Activision" "Konami" "Nintendo"
## [51,] "2K Games" "Activision" "Konami" "Nintendo"
## [52,] "2K Games" "Activision" "Konami" "Square Enix"
## [53,] "2K Games" "Activision" "Moon Studios" "Nintendo"
## [54,] "2K Games" "Activision" "Moon Studios" "Nintendo"
## [55,] "2K Games" "Activision" "Moon Studios" "Square Enix"
## [56,] "2K Games" "Activision" "Nintendo" "Square Enix"
## [57,] "2K Games" "Blizzard" "EA" "From Software"
## [58,] "2K Games" "Blizzard" "EA" "From Software"
## [59,] "2K Games" "Blizzard" "EA" "From Software"
## [60,] "2K Games" "Blizzard" "EA" "From Software"
## [61,] "2K Games" "Blizzard" "EA" "From Software"
## [62,] "2K Games" "Blizzard" "EA" "Konami"
## [63,] "2K Games" "Blizzard" "EA" "Konami"
## [64,] "2K Games" "Blizzard" "EA" "Konami"
## [65,] "2K Games" "Blizzard" "EA" "Konami"
## [66,] "2K Games" "Blizzard" "EA" "Moon Studios"
## [67,] "2K Games" "Blizzard" "EA" "Moon Studios"
## [68,] "2K Games" "Blizzard" "EA" "Moon Studios"
## [69,] "2K Games" "Blizzard" "EA" "Nintendo"
## [70,] "2K Games" "Blizzard" "EA" "Nintendo"
## [71,] "2K Games" "Blizzard" "EA" "Square Enix"
## [72,] "2K Games" "Blizzard" "From Software" "Konami"
## [73,] "2K Games" "Blizzard" "From Software" "Konami"
## [74,] "2K Games" "Blizzard" "From Software" "Konami"
## [75,] "2K Games" "Blizzard" "From Software" "Konami"
## [76,] "2K Games" "Blizzard" "From Software" "Moon Studios"
## [77,] "2K Games" "Blizzard" "From Software" "Moon Studios"
## [78,] "2K Games" "Blizzard" "From Software" "Moon Studios"
## [79,] "2K Games" "Blizzard" "From Software" "Nintendo"
## [80,] "2K Games" "Blizzard" "From Software" "Nintendo"
## [81,] "2K Games" "Blizzard" "From Software" "Square Enix"
## [82,] "2K Games" "Blizzard" "Konami" "Moon Studios"
## [83,] "2K Games" "Blizzard" "Konami" "Moon Studios"
## [84,] "2K Games" "Blizzard" "Konami" "Moon Studios"
## [85,] "2K Games" "Blizzard" "Konami" "Nintendo"
## [86,] "2K Games" "Blizzard" "Konami" "Nintendo"
## [87,] "2K Games" "Blizzard" "Konami" "Square Enix"
## [88,] "2K Games" "Blizzard" "Moon Studios" "Nintendo"
## [89,] "2K Games" "Blizzard" "Moon Studios" "Nintendo"
## [90,] "2K Games" "Blizzard" "Moon Studios" "Square Enix"
## [91,] "2K Games" "Blizzard" "Nintendo" "Square Enix"
## [92,] "2K Games" "EA" "From Software" "Konami"
## [93,] "2K Games" "EA" "From Software" "Konami"
## [94,] "2K Games" "EA" "From Software" "Konami"
## [95,] "2K Games" "EA" "From Software" "Konami"
## [96,] "2K Games" "EA" "From Software" "Moon Studios"
## [97,] "2K Games" "EA" "From Software" "Moon Studios"
## [98,] "2K Games" "EA" "From Software" "Moon Studios"
## [99,] "2K Games" "EA" "From Software" "Nintendo"
## [100,] "2K Games" "EA" "From Software" "Nintendo"
## [101,] "2K Games" "EA" "From Software" "Square Enix"
## [102,] "2K Games" "EA" "Konami" "Moon Studios"
## [103,] "2K Games" "EA" "Konami" "Moon Studios"
## [104,] "2K Games" "EA" "Konami" "Moon Studios"
## [105,] "2K Games" "EA" "Konami" "Nintendo"
## [106,] "2K Games" "EA" "Konami" "Nintendo"
## [107,] "2K Games" "EA" "Konami" "Square Enix"
## [108,] "2K Games" "EA" "Moon Studios" "Nintendo"
## [109,] "2K Games" "EA" "Moon Studios" "Nintendo"
## [110,] "2K Games" "EA" "Moon Studios" "Square Enix"
## [111,] "2K Games" "EA" "Nintendo" "Square Enix"
## [112,] "2K Games" "From Software" "Konami" "Moon Studios"
## [113,] "2K Games" "From Software" "Konami" "Moon Studios"
## [114,] "2K Games" "From Software" "Konami" "Moon Studios"
## [115,] "2K Games" "From Software" "Konami" "Nintendo"
## [116,] "2K Games" "From Software" "Konami" "Nintendo"
## [117,] "2K Games" "From Software" "Konami" "Square Enix"
## [118,] "2K Games" "From Software" "Moon Studios" "Nintendo"
## [119,] "2K Games" "From Software" "Moon Studios" "Nintendo"
## [120,] "2K Games" "From Software" "Moon Studios" "Square Enix"
## [121,] "2K Games" "From Software" "Nintendo" "Square Enix"
## [122,] "2K Games" "Konami" "Moon Studios" "Nintendo"
## [123,] "2K Games" "Konami" "Moon Studios" "Nintendo"
## [124,] "2K Games" "Konami" "Moon Studios" "Square Enix"
## [125,] "2K Games" "Konami" "Nintendo" "Square Enix"
## [126,] "2K Games" "Moon Studios" "Nintendo" "Square Enix"
## [127,] "Activision" "Blizzard" "EA" "From Software"
## [128,] "Activision" "Blizzard" "EA" "From Software"
## [129,] "Activision" "Blizzard" "EA" "From Software"
## [130,] "Activision" "Blizzard" "EA" "From Software"
## [131,] "Activision" "Blizzard" "EA" "From Software"
## [132,] "Activision" "Blizzard" "EA" "Konami"
## [133,] "Activision" "Blizzard" "EA" "Konami"
## [134,] "Activision" "Blizzard" "EA" "Konami"
## [135,] "Activision" "Blizzard" "EA" "Konami"
## [136,] "Activision" "Blizzard" "EA" "Moon Studios"
## [137,] "Activision" "Blizzard" "EA" "Moon Studios"
## [138,] "Activision" "Blizzard" "EA" "Moon Studios"
## [139,] "Activision" "Blizzard" "EA" "Nintendo"
## [140,] "Activision" "Blizzard" "EA" "Nintendo"
## [141,] "Activision" "Blizzard" "EA" "Square Enix"
## [142,] "Activision" "Blizzard" "From Software" "Konami"
## [143,] "Activision" "Blizzard" "From Software" "Konami"
## [144,] "Activision" "Blizzard" "From Software" "Konami"
## [145,] "Activision" "Blizzard" "From Software" "Konami"
## [146,] "Activision" "Blizzard" "From Software" "Moon Studios"
## [147,] "Activision" "Blizzard" "From Software" "Moon Studios"
## [148,] "Activision" "Blizzard" "From Software" "Moon Studios"
## [149,] "Activision" "Blizzard" "From Software" "Nintendo"
## [150,] "Activision" "Blizzard" "From Software" "Nintendo"
## [151,] "Activision" "Blizzard" "From Software" "Square Enix"
## [152,] "Activision" "Blizzard" "Konami" "Moon Studios"
## [153,] "Activision" "Blizzard" "Konami" "Moon Studios"
## [154,] "Activision" "Blizzard" "Konami" "Moon Studios"
## [155,] "Activision" "Blizzard" "Konami" "Nintendo"
## [156,] "Activision" "Blizzard" "Konami" "Nintendo"
## [157,] "Activision" "Blizzard" "Konami" "Square Enix"
## [158,] "Activision" "Blizzard" "Moon Studios" "Nintendo"
## [159,] "Activision" "Blizzard" "Moon Studios" "Nintendo"
## [160,] "Activision" "Blizzard" "Moon Studios" "Square Enix"
## [161,] "Activision" "Blizzard" "Nintendo" "Square Enix"
## [162,] "Activision" "EA" "From Software" "Konami"
## [163,] "Activision" "EA" "From Software" "Konami"
## [164,] "Activision" "EA" "From Software" "Konami"
## [165,] "Activision" "EA" "From Software" "Konami"
## [166,] "Activision" "EA" "From Software" "Moon Studios"
## [167,] "Activision" "EA" "From Software" "Moon Studios"
## [168,] "Activision" "EA" "From Software" "Moon Studios"
## [169,] "Activision" "EA" "From Software" "Nintendo"
## [170,] "Activision" "EA" "From Software" "Nintendo"
## [171,] "Activision" "EA" "From Software" "Square Enix"
## [172,] "Activision" "EA" "Konami" "Moon Studios"
## [173,] "Activision" "EA" "Konami" "Moon Studios"
## [174,] "Activision" "EA" "Konami" "Moon Studios"
## [175,] "Activision" "EA" "Konami" "Nintendo"
## [176,] "Activision" "EA" "Konami" "Nintendo"
## [177,] "Activision" "EA" "Konami" "Square Enix"
## [178,] "Activision" "EA" "Moon Studios" "Nintendo"
## [179,] "Activision" "EA" "Moon Studios" "Nintendo"
## [180,] "Activision" "EA" "Moon Studios" "Square Enix"
## [181,] "Activision" "EA" "Nintendo" "Square Enix"
## [182,] "Activision" "From Software" "Konami" "Moon Studios"
## [183,] "Activision" "From Software" "Konami" "Moon Studios"
## [184,] "Activision" "From Software" "Konami" "Moon Studios"
## [185,] "Activision" "From Software" "Konami" "Nintendo"
## [186,] "Activision" "From Software" "Konami" "Nintendo"
## [187,] "Activision" "From Software" "Konami" "Square Enix"
## [188,] "Activision" "From Software" "Moon Studios" "Nintendo"
## [189,] "Activision" "From Software" "Moon Studios" "Nintendo"
## [190,] "Activision" "From Software" "Moon Studios" "Square Enix"
## [191,] "Activision" "From Software" "Nintendo" "Square Enix"
## [192,] "Activision" "Konami" "Moon Studios" "Nintendo"
## [193,] "Activision" "Konami" "Moon Studios" "Nintendo"
## [194,] "Activision" "Konami" "Moon Studios" "Square Enix"
## [195,] "Activision" "Konami" "Nintendo" "Square Enix"
## [196,] "Activision" "Moon Studios" "Nintendo" "Square Enix"
## [197,] "Blizzard" "EA" "From Software" "Konami"
## [198,] "Blizzard" "EA" "From Software" "Konami"
## [199,] "Blizzard" "EA" "From Software" "Konami"
## [200,] "Blizzard" "EA" "From Software" "Konami"
## [201,] "Blizzard" "EA" "From Software" "Moon Studios"
## [202,] "Blizzard" "EA" "From Software" "Moon Studios"
## [203,] "Blizzard" "EA" "From Software" "Moon Studios"
## [204,] "Blizzard" "EA" "From Software" "Nintendo"
## [205,] "Blizzard" "EA" "From Software" "Nintendo"
## [206,] "Blizzard" "EA" "From Software" "Square Enix"
## [207,] "Blizzard" "EA" "Konami" "Moon Studios"
## [208,] "Blizzard" "EA" "Konami" "Moon Studios"
## [209,] "Blizzard" "EA" "Konami" "Moon Studios"
## [210,] "Blizzard" "EA" "Konami" "Nintendo"
## [211,] "Blizzard" "EA" "Konami" "Nintendo"
## [212,] "Blizzard" "EA" "Konami" "Square Enix"
## [213,] "Blizzard" "EA" "Moon Studios" "Nintendo"
## [214,] "Blizzard" "EA" "Moon Studios" "Nintendo"
## [215,] "Blizzard" "EA" "Moon Studios" "Square Enix"
## [216,] "Blizzard" "EA" "Nintendo" "Square Enix"
## [217,] "Blizzard" "From Software" "Konami" "Moon Studios"
## [218,] "Blizzard" "From Software" "Konami" "Moon Studios"
## [219,] "Blizzard" "From Software" "Konami" "Moon Studios"
## [220,] "Blizzard" "From Software" "Konami" "Nintendo"
## [221,] "Blizzard" "From Software" "Konami" "Nintendo"
## [222,] "Blizzard" "From Software" "Konami" "Square Enix"
## [223,] "Blizzard" "From Software" "Moon Studios" "Nintendo"
## [224,] "Blizzard" "From Software" "Moon Studios" "Nintendo"
## [225,] "Blizzard" "From Software" "Moon Studios" "Square Enix"
## [226,] "Blizzard" "From Software" "Nintendo" "Square Enix"
## [227,] "Blizzard" "Konami" "Moon Studios" "Nintendo"
## [228,] "Blizzard" "Konami" "Moon Studios" "Nintendo"
## [229,] "Blizzard" "Konami" "Moon Studios" "Square Enix"
## [230,] "Blizzard" "Konami" "Nintendo" "Square Enix"
## [231,] "Blizzard" "Moon Studios" "Nintendo" "Square Enix"
## [232,] "EA" "From Software" "Konami" "Moon Studios"
## [233,] "EA" "From Software" "Konami" "Moon Studios"
## [234,] "EA" "From Software" "Konami" "Moon Studios"
## [235,] "EA" "From Software" "Konami" "Nintendo"
## [236,] "EA" "From Software" "Konami" "Nintendo"
## [237,] "EA" "From Software" "Konami" "Square Enix"
## [238,] "EA" "From Software" "Moon Studios" "Nintendo"
## [239,] "EA" "From Software" "Moon Studios" "Nintendo"
## [240,] "EA" "From Software" "Moon Studios" "Square Enix"
## [241,] "EA" "From Software" "Nintendo" "Square Enix"
## [242,] "EA" "Konami" "Moon Studios" "Nintendo"
## [243,] "EA" "Konami" "Moon Studios" "Nintendo"
## [244,] "EA" "Konami" "Moon Studios" "Square Enix"
## [245,] "EA" "Konami" "Nintendo" "Square Enix"
## [246,] "EA" "Moon Studios" "Nintendo" "Square Enix"
## [247,] "From Software" "Konami" "Moon Studios" "Nintendo"
## [248,] "From Software" "Konami" "Moon Studios" "Nintendo"
## [249,] "From Software" "Konami" "Moon Studios" "Square Enix"
## [250,] "From Software" "Konami" "Nintendo" "Square Enix"
## [251,] "From Software" "Moon Studios" "Nintendo" "Square Enix"
## [252,] "Konami" "Moon Studios" "Nintendo" "Square Enix"
## [,5]
## [1,] "From Software"
## [2,] "Konami"
## [3,] "Moon Studios"
## [4,] "Nintendo"
## [5,] "Square Enix"
## [6,] "Ubisoft"
## [7,] "Konami"
## [8,] "Moon Studios"
## [9,] "Nintendo"
## [10,] "Square Enix"
## [11,] "Ubisoft"
## [12,] "Moon Studios"
## [13,] "Nintendo"
## [14,] "Square Enix"
## [15,] "Ubisoft"
## [16,] "Nintendo"
## [17,] "Square Enix"
## [18,] "Ubisoft"
## [19,] "Square Enix"
## [20,] "Ubisoft"
## [21,] "Ubisoft"
## [22,] "Konami"
## [23,] "Moon Studios"
## [24,] "Nintendo"
## [25,] "Square Enix"
## [26,] "Ubisoft"
## [27,] "Moon Studios"
## [28,] "Nintendo"
## [29,] "Square Enix"
## [30,] "Ubisoft"
## [31,] "Nintendo"
## [32,] "Square Enix"
## [33,] "Ubisoft"
## [34,] "Square Enix"
## [35,] "Ubisoft"
## [36,] "Ubisoft"
## [37,] "Moon Studios"
## [38,] "Nintendo"
## [39,] "Square Enix"
## [40,] "Ubisoft"
## [41,] "Nintendo"
## [42,] "Square Enix"
## [43,] "Ubisoft"
## [44,] "Square Enix"
## [45,] "Ubisoft"
## [46,] "Ubisoft"
## [47,] "Nintendo"
## [48,] "Square Enix"
## [49,] "Ubisoft"
## [50,] "Square Enix"
## [51,] "Ubisoft"
## [52,] "Ubisoft"
## [53,] "Square Enix"
## [54,] "Ubisoft"
## [55,] "Ubisoft"
## [56,] "Ubisoft"
## [57,] "Konami"
## [58,] "Moon Studios"
## [59,] "Nintendo"
## [60,] "Square Enix"
## [61,] "Ubisoft"
## [62,] "Moon Studios"
## [63,] "Nintendo"
## [64,] "Square Enix"
## [65,] "Ubisoft"
## [66,] "Nintendo"
## [67,] "Square Enix"
## [68,] "Ubisoft"
## [69,] "Square Enix"
## [70,] "Ubisoft"
## [71,] "Ubisoft"
## [72,] "Moon Studios"
## [73,] "Nintendo"
## [74,] "Square Enix"
## [75,] "Ubisoft"
## [76,] "Nintendo"
## [77,] "Square Enix"
## [78,] "Ubisoft"
## [79,] "Square Enix"
## [80,] "Ubisoft"
## [81,] "Ubisoft"
## [82,] "Nintendo"
## [83,] "Square Enix"
## [84,] "Ubisoft"
## [85,] "Square Enix"
## [86,] "Ubisoft"
## [87,] "Ubisoft"
## [88,] "Square Enix"
## [89,] "Ubisoft"
## [90,] "Ubisoft"
## [91,] "Ubisoft"
## [92,] "Moon Studios"
## [93,] "Nintendo"
## [94,] "Square Enix"
## [95,] "Ubisoft"
## [96,] "Nintendo"
## [97,] "Square Enix"
## [98,] "Ubisoft"
## [99,] "Square Enix"
## [100,] "Ubisoft"
## [101,] "Ubisoft"
## [102,] "Nintendo"
## [103,] "Square Enix"
## [104,] "Ubisoft"
## [105,] "Square Enix"
## [106,] "Ubisoft"
## [107,] "Ubisoft"
## [108,] "Square Enix"
## [109,] "Ubisoft"
## [110,] "Ubisoft"
## [111,] "Ubisoft"
## [112,] "Nintendo"
## [113,] "Square Enix"
## [114,] "Ubisoft"
## [115,] "Square Enix"
## [116,] "Ubisoft"
## [117,] "Ubisoft"
## [118,] "Square Enix"
## [119,] "Ubisoft"
## [120,] "Ubisoft"
## [121,] "Ubisoft"
## [122,] "Square Enix"
## [123,] "Ubisoft"
## [124,] "Ubisoft"
## [125,] "Ubisoft"
## [126,] "Ubisoft"
## [127,] "Konami"
## [128,] "Moon Studios"
## [129,] "Nintendo"
## [130,] "Square Enix"
## [131,] "Ubisoft"
## [132,] "Moon Studios"
## [133,] "Nintendo"
## [134,] "Square Enix"
## [135,] "Ubisoft"
## [136,] "Nintendo"
## [137,] "Square Enix"
## [138,] "Ubisoft"
## [139,] "Square Enix"
## [140,] "Ubisoft"
## [141,] "Ubisoft"
## [142,] "Moon Studios"
## [143,] "Nintendo"
## [144,] "Square Enix"
## [145,] "Ubisoft"
## [146,] "Nintendo"
## [147,] "Square Enix"
## [148,] "Ubisoft"
## [149,] "Square Enix"
## [150,] "Ubisoft"
## [151,] "Ubisoft"
## [152,] "Nintendo"
## [153,] "Square Enix"
## [154,] "Ubisoft"
## [155,] "Square Enix"
## [156,] "Ubisoft"
## [157,] "Ubisoft"
## [158,] "Square Enix"
## [159,] "Ubisoft"
## [160,] "Ubisoft"
## [161,] "Ubisoft"
## [162,] "Moon Studios"
## [163,] "Nintendo"
## [164,] "Square Enix"
## [165,] "Ubisoft"
## [166,] "Nintendo"
## [167,] "Square Enix"
## [168,] "Ubisoft"
## [169,] "Square Enix"
## [170,] "Ubisoft"
## [171,] "Ubisoft"
## [172,] "Nintendo"
## [173,] "Square Enix"
## [174,] "Ubisoft"
## [175,] "Square Enix"
## [176,] "Ubisoft"
## [177,] "Ubisoft"
## [178,] "Square Enix"
## [179,] "Ubisoft"
## [180,] "Ubisoft"
## [181,] "Ubisoft"
## [182,] "Nintendo"
## [183,] "Square Enix"
## [184,] "Ubisoft"
## [185,] "Square Enix"
## [186,] "Ubisoft"
## [187,] "Ubisoft"
## [188,] "Square Enix"
## [189,] "Ubisoft"
## [190,] "Ubisoft"
## [191,] "Ubisoft"
## [192,] "Square Enix"
## [193,] "Ubisoft"
## [194,] "Ubisoft"
## [195,] "Ubisoft"
## [196,] "Ubisoft"
## [197,] "Moon Studios"
## [198,] "Nintendo"
## [199,] "Square Enix"
## [200,] "Ubisoft"
## [201,] "Nintendo"
## [202,] "Square Enix"
## [203,] "Ubisoft"
## [204,] "Square Enix"
## [205,] "Ubisoft"
## [206,] "Ubisoft"
## [207,] "Nintendo"
## [208,] "Square Enix"
## [209,] "Ubisoft"
## [210,] "Square Enix"
## [211,] "Ubisoft"
## [212,] "Ubisoft"
## [213,] "Square Enix"
## [214,] "Ubisoft"
## [215,] "Ubisoft"
## [216,] "Ubisoft"
## [217,] "Nintendo"
## [218,] "Square Enix"
## [219,] "Ubisoft"
## [220,] "Square Enix"
## [221,] "Ubisoft"
## [222,] "Ubisoft"
## [223,] "Square Enix"
## [224,] "Ubisoft"
## [225,] "Ubisoft"
## [226,] "Ubisoft"
## [227,] "Square Enix"
## [228,] "Ubisoft"
## [229,] "Ubisoft"
## [230,] "Ubisoft"
## [231,] "Ubisoft"
## [232,] "Nintendo"
## [233,] "Square Enix"
## [234,] "Ubisoft"
## [235,] "Square Enix"
## [236,] "Ubisoft"
## [237,] "Ubisoft"
## [238,] "Square Enix"
## [239,] "Ubisoft"
## [240,] "Ubisoft"
## [241,] "Ubisoft"
## [242,] "Square Enix"
## [243,] "Ubisoft"
## [244,] "Ubisoft"
## [245,] "Ubisoft"
## [246,] "Ubisoft"
## [247,] "Square Enix"
## [248,] "Ubisoft"
## [249,] "Ubisoft"
## [250,] "Ubisoft"
## [251,] "Ubisoft"
## [252,] "Ubisoft"¿Para qué sirve encontrar el número de combinaciones y la forma en que se agrupan?
Eso sería el espacio muestral que ya construído éste, permite hacer interpretaciones en términos probabilísticos.
5 Interpretación
El resultado de las combinaciones permite construir un espacio muestral que ofrece la oportunidad de conocer en términos de probabilidad, la cantidad de ocasiones y lo que representa un evento conforme a todo el espacio muestral, es decir frecuencia y frecuencia porcentual.
5.1 Preguntas sobre espacio muestral nombres
¿En cuántas ocasiones aparece el nombre de Laura en combinaciones de dos en dos?.
resultado = subset(Cn.nombres, Cn.nombres[,1] == "Laura" |
Cn.nombres[,2] == "Laura")
resultado## [,1] [,2]
## [1,] "Alberto" "Laura"
## [2,] "Andrés" "Laura"
## [3,] "Emilio" "Laura"
## [4,] "Fani" "Laura"
## [5,] "Juan" "Laura"
## [6,] "Laura" "Lucy"
## [7,] "Laura" "Oscar"
## [8,] "Laura" "Paco"
## [9,] "Laura" "Paty"
## [10,] "Laura" "Rubén"
## [11,] "Laura" "Sebastián"
## [12,] "Laura" "Yareli"
## [13,] "Laura" "Yariel"frecuencia = nrow(resultado)
paste("Asumiendo que buscaremos en ambas columnas, aparece un total de",frecuencia,"veces")## [1] "Asumiendo que buscaremos en ambas columnas, aparece un total de 13 veces"¿En cuántas ocasiones aparece el nombre de Oscar en las combinaciones de dos en dos?
resultado = subset(Cn.nombres, Cn.nombres[,1] == "Oscar" |
Cn.nombres[,2] == "Oscar")
resultado## [,1] [,2]
## [1,] "Alberto" "Oscar"
## [2,] "Andrés" "Oscar"
## [3,] "Emilio" "Oscar"
## [4,] "Fani" "Oscar"
## [5,] "Juan" "Oscar"
## [6,] "Laura" "Oscar"
## [7,] "Lucy" "Oscar"
## [8,] "Oscar" "Paco"
## [9,] "Oscar" "Paty"
## [10,] "Oscar" "Rubén"
## [11,] "Oscar" "Sebastián"
## [12,] "Oscar" "Yareli"
## [13,] "Oscar" "Yariel"frecuencia = nrow(resultado)
paste("Asumiendo que buscaremos en ambas columnas, aparece un total de",frecuencia,"veces")## [1] "Asumiendo que buscaremos en ambas columnas, aparece un total de 13 veces"En las combinaciones de nombres de dos en dos, ¿en cuántas ocasiones existe Laura y Oscar juntos o contiguos y en ese orden?.
resultado = subset(Cn.nombres,
Cn.nombres[,1] == "Laura" &
Cn.nombres[,2] == "Oscar"
)
resultado## [,1] [,2]
## [1,] "Laura" "Oscar"frecuencia = nrow(resultado)
paste("Si buscamos a Laura y a Oscar en ese orden y juntos, solo los encontramos en",frecuencia, "ocasión de",nrow(Cn.nombres),", que representa el",round(frecuencia * 100 / nrow(Cn.nombres),2),"%")## [1] "Si buscamos a Laura y a Oscar en ese orden y juntos, solo los encontramos en 1 ocasión de 91 , que representa el 1.1 %"Se utiliza la función subset() para hacer filtros y responder a las preguntas.
La nominación [ , ] significa acceder al valor de un data frame por la primer columna y [ ,2] la segunda columna.
En las combinaciones de nombres de dos en dos, ¿en cuántas ocasiones existe Sebastián en la primer columna de todo el espacio muestral?
resultado = subset(Cn.nombres, Cn.nombres[,1] == "Sebastián")
resultado## [,1] [,2]
## [1,] "Sebastián" "Yareli"
## [2,] "Sebastián" "Yariel"frecuencia = nrow(resultado)
paste("Buscando en la primer columna, encontramos a Sebastián",frecuencia,"veces de",nrow(Cn.nombres),"que representan el",round(frecuencia * 100 / nrow(Cn.nombres),2),"%")## [1] "Buscando en la primer columna, encontramos a Sebastián 2 veces de 91 que representan el 2.2 %"En cuántas ocasiones aparece en primera columna Oscar y Yariel o Sebastián en segunda columna
resultado = subset(Cn.nombres, Cn.nombres[,1] == "Oscar" &
(Cn.nombres[,2] == "Yariel" | Cn.nombres[,2] == "Sebastián"))
resultado## [,1] [,2]
## [1,] "Oscar" "Sebastián"
## [2,] "Oscar" "Yariel"frecuencia = nrow(resultado)
paste("Buscando a Oscar en la primera columna, y junto a él Yariel o Sebastián en la segunda, los encontramos",frecuencia ,"veces de",nrow(Cn.nombres) ,"que representan el", round(frecuencia * 100 / nrow(Cn.nombres), 2), "%")## [1] "Buscando a Oscar en la primera columna, y junto a él Yariel o Sebastián en la segunda, los encontramos 2 veces de 91 que representan el 2.2 %"5.2 Preguntas sobre espacio muestral compañías
En cuántas ocasiones aparece de manera contigua y en este orden los equipos de Activision y Konami en primera y segunda columna respectivamente.
resultado = subset(Cn.empresas,
Cn.empresas[,1] == "Activision" &
Cn.empresas[,2] == "Konami")
resultado## [,1] [,2] [,3] [,4] [,5]
## [1,] "Activision" "Konami" "Moon Studios" "Nintendo" "Square Enix"
## [2,] "Activision" "Konami" "Moon Studios" "Nintendo" "Ubisoft"
## [3,] "Activision" "Konami" "Moon Studios" "Square Enix" "Ubisoft"
## [4,] "Activision" "Konami" "Nintendo" "Square Enix" "Ubisoft"frecuencia = nrow(resultado)
paste("Buscando en la primera y segunda columna los nombres de Activision y Konami respectivamente, los encontramos", frecuencia, "veces de un total de", nrow(Cn.empresas), ", lo que representa el",round(frecuencia * 100 / nrow(Cn.empresas), 2), "%")## [1] "Buscando en la primera y segunda columna los nombres de Activision y Konami respectivamente, los encontramos 4 veces de un total de 252 , lo que representa el 1.59 %"En cuántas ocasiones aparece de manera contigua y en este orden los equipos de Activision y Blizzard en primera y segunda columna respectivamente.
resultado = subset(Cn.empresas,
Cn.empresas[,1] == "Activision" &
Cn.empresas[,2] == "Blizzard")
resultado## [,1] [,2] [,3] [,4] [,5]
## [1,] "Activision" "Blizzard" "EA" "From Software" "Konami"
## [2,] "Activision" "Blizzard" "EA" "From Software" "Moon Studios"
## [3,] "Activision" "Blizzard" "EA" "From Software" "Nintendo"
## [4,] "Activision" "Blizzard" "EA" "From Software" "Square Enix"
## [5,] "Activision" "Blizzard" "EA" "From Software" "Ubisoft"
## [6,] "Activision" "Blizzard" "EA" "Konami" "Moon Studios"
## [7,] "Activision" "Blizzard" "EA" "Konami" "Nintendo"
## [8,] "Activision" "Blizzard" "EA" "Konami" "Square Enix"
## [9,] "Activision" "Blizzard" "EA" "Konami" "Ubisoft"
## [10,] "Activision" "Blizzard" "EA" "Moon Studios" "Nintendo"
## [11,] "Activision" "Blizzard" "EA" "Moon Studios" "Square Enix"
## [12,] "Activision" "Blizzard" "EA" "Moon Studios" "Ubisoft"
## [13,] "Activision" "Blizzard" "EA" "Nintendo" "Square Enix"
## [14,] "Activision" "Blizzard" "EA" "Nintendo" "Ubisoft"
## [15,] "Activision" "Blizzard" "EA" "Square Enix" "Ubisoft"
## [16,] "Activision" "Blizzard" "From Software" "Konami" "Moon Studios"
## [17,] "Activision" "Blizzard" "From Software" "Konami" "Nintendo"
## [18,] "Activision" "Blizzard" "From Software" "Konami" "Square Enix"
## [19,] "Activision" "Blizzard" "From Software" "Konami" "Ubisoft"
## [20,] "Activision" "Blizzard" "From Software" "Moon Studios" "Nintendo"
## [21,] "Activision" "Blizzard" "From Software" "Moon Studios" "Square Enix"
## [22,] "Activision" "Blizzard" "From Software" "Moon Studios" "Ubisoft"
## [23,] "Activision" "Blizzard" "From Software" "Nintendo" "Square Enix"
## [24,] "Activision" "Blizzard" "From Software" "Nintendo" "Ubisoft"
## [25,] "Activision" "Blizzard" "From Software" "Square Enix" "Ubisoft"
## [26,] "Activision" "Blizzard" "Konami" "Moon Studios" "Nintendo"
## [27,] "Activision" "Blizzard" "Konami" "Moon Studios" "Square Enix"
## [28,] "Activision" "Blizzard" "Konami" "Moon Studios" "Ubisoft"
## [29,] "Activision" "Blizzard" "Konami" "Nintendo" "Square Enix"
## [30,] "Activision" "Blizzard" "Konami" "Nintendo" "Ubisoft"
## [31,] "Activision" "Blizzard" "Konami" "Square Enix" "Ubisoft"
## [32,] "Activision" "Blizzard" "Moon Studios" "Nintendo" "Square Enix"
## [33,] "Activision" "Blizzard" "Moon Studios" "Nintendo" "Ubisoft"
## [34,] "Activision" "Blizzard" "Moon Studios" "Square Enix" "Ubisoft"
## [35,] "Activision" "Blizzard" "Nintendo" "Square Enix" "Ubisoft"frecuencia = nrow(resultado)
paste("Buscando en la primera y segunda columna los nombres de Activision y Blizzard respectivamente, los encontramos", frecuencia, "veces de un total de", nrow(Cn.empresas), ", lo que representa el",round(frecuencia * 100 / nrow(Cn.empresas), 2), "%")## [1] "Buscando en la primera y segunda columna los nombres de Activision y Blizzard respectivamente, los encontramos 35 veces de un total de 252 , lo que representa el 13.89 %"¿En cuántas ocasiones aparece de manera contigua y en este orden los equipos de Activision y Blizzard en cualquier columna uno y dos, dos y tres, tres y cuatro o cuatro y cinco?
resultado = subset(Cn.empresas, (
Cn.empresas[,1] == "Activision" &
Cn.empresas[,2] == "Blizzard"
) | (
Cn.empresas[,2] == "Activision" &
Cn.empresas[,3] == "Blizzard"
) | (
Cn.empresas[,3] == "Activision" &
Cn.empresas[,4] == "Blizzard"
) | (
Cn.empresas[,4] == "Activision" &
Cn.empresas[,5] == "Blizzard"
)
)
resultado## [,1] [,2] [,3] [,4] [,5]
## [1,] "2K Games" "Activision" "Blizzard" "EA" "From Software"
## [2,] "2K Games" "Activision" "Blizzard" "EA" "Konami"
## [3,] "2K Games" "Activision" "Blizzard" "EA" "Moon Studios"
## [4,] "2K Games" "Activision" "Blizzard" "EA" "Nintendo"
## [5,] "2K Games" "Activision" "Blizzard" "EA" "Square Enix"
## [6,] "2K Games" "Activision" "Blizzard" "EA" "Ubisoft"
## [7,] "2K Games" "Activision" "Blizzard" "From Software" "Konami"
## [8,] "2K Games" "Activision" "Blizzard" "From Software" "Moon Studios"
## [9,] "2K Games" "Activision" "Blizzard" "From Software" "Nintendo"
## [10,] "2K Games" "Activision" "Blizzard" "From Software" "Square Enix"
## [11,] "2K Games" "Activision" "Blizzard" "From Software" "Ubisoft"
## [12,] "2K Games" "Activision" "Blizzard" "Konami" "Moon Studios"
## [13,] "2K Games" "Activision" "Blizzard" "Konami" "Nintendo"
## [14,] "2K Games" "Activision" "Blizzard" "Konami" "Square Enix"
## [15,] "2K Games" "Activision" "Blizzard" "Konami" "Ubisoft"
## [16,] "2K Games" "Activision" "Blizzard" "Moon Studios" "Nintendo"
## [17,] "2K Games" "Activision" "Blizzard" "Moon Studios" "Square Enix"
## [18,] "2K Games" "Activision" "Blizzard" "Moon Studios" "Ubisoft"
## [19,] "2K Games" "Activision" "Blizzard" "Nintendo" "Square Enix"
## [20,] "2K Games" "Activision" "Blizzard" "Nintendo" "Ubisoft"
## [21,] "2K Games" "Activision" "Blizzard" "Square Enix" "Ubisoft"
## [22,] "Activision" "Blizzard" "EA" "From Software" "Konami"
## [23,] "Activision" "Blizzard" "EA" "From Software" "Moon Studios"
## [24,] "Activision" "Blizzard" "EA" "From Software" "Nintendo"
## [25,] "Activision" "Blizzard" "EA" "From Software" "Square Enix"
## [26,] "Activision" "Blizzard" "EA" "From Software" "Ubisoft"
## [27,] "Activision" "Blizzard" "EA" "Konami" "Moon Studios"
## [28,] "Activision" "Blizzard" "EA" "Konami" "Nintendo"
## [29,] "Activision" "Blizzard" "EA" "Konami" "Square Enix"
## [30,] "Activision" "Blizzard" "EA" "Konami" "Ubisoft"
## [31,] "Activision" "Blizzard" "EA" "Moon Studios" "Nintendo"
## [32,] "Activision" "Blizzard" "EA" "Moon Studios" "Square Enix"
## [33,] "Activision" "Blizzard" "EA" "Moon Studios" "Ubisoft"
## [34,] "Activision" "Blizzard" "EA" "Nintendo" "Square Enix"
## [35,] "Activision" "Blizzard" "EA" "Nintendo" "Ubisoft"
## [36,] "Activision" "Blizzard" "EA" "Square Enix" "Ubisoft"
## [37,] "Activision" "Blizzard" "From Software" "Konami" "Moon Studios"
## [38,] "Activision" "Blizzard" "From Software" "Konami" "Nintendo"
## [39,] "Activision" "Blizzard" "From Software" "Konami" "Square Enix"
## [40,] "Activision" "Blizzard" "From Software" "Konami" "Ubisoft"
## [41,] "Activision" "Blizzard" "From Software" "Moon Studios" "Nintendo"
## [42,] "Activision" "Blizzard" "From Software" "Moon Studios" "Square Enix"
## [43,] "Activision" "Blizzard" "From Software" "Moon Studios" "Ubisoft"
## [44,] "Activision" "Blizzard" "From Software" "Nintendo" "Square Enix"
## [45,] "Activision" "Blizzard" "From Software" "Nintendo" "Ubisoft"
## [46,] "Activision" "Blizzard" "From Software" "Square Enix" "Ubisoft"
## [47,] "Activision" "Blizzard" "Konami" "Moon Studios" "Nintendo"
## [48,] "Activision" "Blizzard" "Konami" "Moon Studios" "Square Enix"
## [49,] "Activision" "Blizzard" "Konami" "Moon Studios" "Ubisoft"
## [50,] "Activision" "Blizzard" "Konami" "Nintendo" "Square Enix"
## [51,] "Activision" "Blizzard" "Konami" "Nintendo" "Ubisoft"
## [52,] "Activision" "Blizzard" "Konami" "Square Enix" "Ubisoft"
## [53,] "Activision" "Blizzard" "Moon Studios" "Nintendo" "Square Enix"
## [54,] "Activision" "Blizzard" "Moon Studios" "Nintendo" "Ubisoft"
## [55,] "Activision" "Blizzard" "Moon Studios" "Square Enix" "Ubisoft"
## [56,] "Activision" "Blizzard" "Nintendo" "Square Enix" "Ubisoft"frecuencia = nrow(resultado)
paste("Buscando en columnas contiguas los nombres de Activision y Blizzard respectivamente, los encontramos", frecuencia, "veces de un total de", nrow(Cn.empresas), ", lo que representa el",round(frecuencia * 100 / nrow(Cn.empresas), 2), "%")## [1] "Buscando en columnas contiguas los nombres de Activision y Blizzard respectivamente, los encontramos 56 veces de un total de 252 , lo que representa el 22.22 %"6 Bibliografía
Anderson, David R., Dennis J. Sweeney, and Thomas A. Williams. 2008. Estadística Para Administración y Economía. 10th ed. Australia Brasil Corea España Estados Unidos Japón México Reino Unido Singapur: Cengage Learning,.
Mendenhall, William, Robert J. Beaver, and Barbara M. Beaver. 2010. Introducción a La Probabilidad y Estadística. 13th ed. Cengage Learning Editores, S.A. de C.V.,.
Walpole, Ronald E., Raymond H. Myers, and Sharon L. Myers. 2012. Probabilidad y Estadística Para Ingeniería y Ciencias. Novena Edición. México: Pearson.
Anderson, David R., Dennis J. Sweeney, and Thomas A. Williams. 2008.
Estadística Para Administración y Economía. 10th ed. Australia
Brasil Corea España
Estados Unidos Japón México
Reino Unido Singapur: Cengage Learning,.
Mendenhall, William, Robert J. Beaver, and Barbara M. Beaver. 2010.
Introducción a La Probabilidad y Estadística. 13th ed. Cengage
Learning Editores, S.A. de C.V.,.
Walpole, Ronald E., Raymond H. Myers, and Sharon L. Myers. 2012.
Probabilidad y Estadística Para Ingeniería y Ciencias. Novena
Edición. México: Pearson.