1.- Cargar librerías

library(gtools)
## Warning: package 'gtools' was built under R version 3.6.3
library(knitr)
## Warning: package 'knitr' was built under R version 3.6.3

2.- Construir datos

S.personas <- c("Juan", "Paty", "Laura", "Oscar", "Aracely")

personas.agregadas <- c("Jose", "Marcos", "Ruby", "Fernanda", "Adrian")

S.personas <- c(S.personas,personas.agregadas)
S.personas
##  [1] "Juan"     "Paty"     "Laura"    "Oscar"    "Aracely"  "Jose"    
##  [7] "Marcos"   "Ruby"     "Fernanda" "Adrian"
n <- length(S.personas)

3.- Realizar Permutaciones con grupos de 3, 5 y 7

Permutaciones de 3

grupos <- 3
head(permutations(n = n,r = grupos, S.personas),10)
##       [,1]     [,2]       [,3]      
##  [1,] "Adrian" "Aracely"  "Fernanda"
##  [2,] "Adrian" "Aracely"  "Jose"    
##  [3,] "Adrian" "Aracely"  "Juan"    
##  [4,] "Adrian" "Aracely"  "Laura"   
##  [5,] "Adrian" "Aracely"  "Marcos"  
##  [6,] "Adrian" "Aracely"  "Oscar"   
##  [7,] "Adrian" "Aracely"  "Paty"    
##  [8,] "Adrian" "Aracely"  "Ruby"    
##  [9,] "Adrian" "Fernanda" "Aracely" 
## [10,] "Adrian" "Fernanda" "Jose"
tail(permutations(n = n,r = grupos, S.personas),10)
##        [,1]   [,2]    [,3]      
## [711,] "Ruby" "Oscar" "Marcos"  
## [712,] "Ruby" "Oscar" "Paty"    
## [713,] "Ruby" "Paty"  "Adrian"  
## [714,] "Ruby" "Paty"  "Aracely" 
## [715,] "Ruby" "Paty"  "Fernanda"
## [716,] "Ruby" "Paty"  "Jose"    
## [717,] "Ruby" "Paty"  "Juan"    
## [718,] "Ruby" "Paty"  "Laura"   
## [719,] "Ruby" "Paty"  "Marcos"  
## [720,] "Ruby" "Paty"  "Oscar"

Permutaciones de 5

grupos <- 5
head(permutations(n = n,r = grupos, S.personas),10)
##       [,1]     [,2]      [,3]       [,4]   [,5]    
##  [1,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan"  
##  [2,] "Adrian" "Aracely" "Fernanda" "Jose" "Laura" 
##  [3,] "Adrian" "Aracely" "Fernanda" "Jose" "Marcos"
##  [4,] "Adrian" "Aracely" "Fernanda" "Jose" "Oscar" 
##  [5,] "Adrian" "Aracely" "Fernanda" "Jose" "Paty"  
##  [6,] "Adrian" "Aracely" "Fernanda" "Jose" "Ruby"  
##  [7,] "Adrian" "Aracely" "Fernanda" "Juan" "Jose"  
##  [8,] "Adrian" "Aracely" "Fernanda" "Juan" "Laura" 
##  [9,] "Adrian" "Aracely" "Fernanda" "Juan" "Marcos"
## [10,] "Adrian" "Aracely" "Fernanda" "Juan" "Oscar"
tail(permutations(n = n,r = grupos, S.personas),10)
##          [,1]   [,2]   [,3]    [,4]     [,5]      
## [30231,] "Ruby" "Paty" "Oscar" "Laura"  "Fernanda"
## [30232,] "Ruby" "Paty" "Oscar" "Laura"  "Jose"    
## [30233,] "Ruby" "Paty" "Oscar" "Laura"  "Juan"    
## [30234,] "Ruby" "Paty" "Oscar" "Laura"  "Marcos"  
## [30235,] "Ruby" "Paty" "Oscar" "Marcos" "Adrian"  
## [30236,] "Ruby" "Paty" "Oscar" "Marcos" "Aracely" 
## [30237,] "Ruby" "Paty" "Oscar" "Marcos" "Fernanda"
## [30238,] "Ruby" "Paty" "Oscar" "Marcos" "Jose"    
## [30239,] "Ruby" "Paty" "Oscar" "Marcos" "Juan"    
## [30240,] "Ruby" "Paty" "Oscar" "Marcos" "Laura"

Permutaciones de 7

grupos <- 7
head(permutations(n = n,r = grupos, S.personas),10)
##       [,1]     [,2]      [,3]       [,4]   [,5]   [,6]     [,7]    
##  [1,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Laura"  "Marcos"
##  [2,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Laura"  "Oscar" 
##  [3,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Laura"  "Paty"  
##  [4,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Laura"  "Ruby"  
##  [5,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Marcos" "Laura" 
##  [6,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Marcos" "Oscar" 
##  [7,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Marcos" "Paty"  
##  [8,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Marcos" "Ruby"  
##  [9,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Oscar"  "Laura" 
## [10,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Oscar"  "Marcos"
tail(permutations(n = n,r = grupos, S.personas),10)
##           [,1]   [,2]   [,3]    [,4]     [,5]    [,6]       [,7]      
## [604791,] "Ruby" "Paty" "Oscar" "Marcos" "Laura" "Fernanda" "Jose"    
## [604792,] "Ruby" "Paty" "Oscar" "Marcos" "Laura" "Fernanda" "Juan"    
## [604793,] "Ruby" "Paty" "Oscar" "Marcos" "Laura" "Jose"     "Adrian"  
## [604794,] "Ruby" "Paty" "Oscar" "Marcos" "Laura" "Jose"     "Aracely" 
## [604795,] "Ruby" "Paty" "Oscar" "Marcos" "Laura" "Jose"     "Fernanda"
## [604796,] "Ruby" "Paty" "Oscar" "Marcos" "Laura" "Jose"     "Juan"    
## [604797,] "Ruby" "Paty" "Oscar" "Marcos" "Laura" "Juan"     "Adrian"  
## [604798,] "Ruby" "Paty" "Oscar" "Marcos" "Laura" "Juan"     "Aracely" 
## [604799,] "Ruby" "Paty" "Oscar" "Marcos" "Laura" "Juan"     "Fernanda"
## [604800,] "Ruby" "Paty" "Oscar" "Marcos" "Laura" "Juan"     "Jose"

4. Realizar combinaciones con grupos de 4, 6 y 8

Combinaciones de 4

grupos <- 4
head(combinations(n = n,r = grupos, S.personas),10)
##       [,1]     [,2]      [,3]       [,4]    
##  [1,] "Adrian" "Aracely" "Fernanda" "Jose"  
##  [2,] "Adrian" "Aracely" "Fernanda" "Juan"  
##  [3,] "Adrian" "Aracely" "Fernanda" "Laura" 
##  [4,] "Adrian" "Aracely" "Fernanda" "Marcos"
##  [5,] "Adrian" "Aracely" "Fernanda" "Oscar" 
##  [6,] "Adrian" "Aracely" "Fernanda" "Paty"  
##  [7,] "Adrian" "Aracely" "Fernanda" "Ruby"  
##  [8,] "Adrian" "Aracely" "Jose"     "Juan"  
##  [9,] "Adrian" "Aracely" "Jose"     "Laura" 
## [10,] "Adrian" "Aracely" "Jose"     "Marcos"
tail(combinations(n = n,r = grupos, S.personas),10)
##        [,1]     [,2]     [,3]    [,4]  
## [201,] "Juan"   "Laura"  "Paty"  "Ruby"
## [202,] "Juan"   "Marcos" "Oscar" "Paty"
## [203,] "Juan"   "Marcos" "Oscar" "Ruby"
## [204,] "Juan"   "Marcos" "Paty"  "Ruby"
## [205,] "Juan"   "Oscar"  "Paty"  "Ruby"
## [206,] "Laura"  "Marcos" "Oscar" "Paty"
## [207,] "Laura"  "Marcos" "Oscar" "Ruby"
## [208,] "Laura"  "Marcos" "Paty"  "Ruby"
## [209,] "Laura"  "Oscar"  "Paty"  "Ruby"
## [210,] "Marcos" "Oscar"  "Paty"  "Ruby"

Combinaciones de 6

grupos <- 5
head(combinations(n = n,r = grupos, S.personas),10)
##       [,1]     [,2]      [,3]       [,4]   [,5]    
##  [1,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan"  
##  [2,] "Adrian" "Aracely" "Fernanda" "Jose" "Laura" 
##  [3,] "Adrian" "Aracely" "Fernanda" "Jose" "Marcos"
##  [4,] "Adrian" "Aracely" "Fernanda" "Jose" "Oscar" 
##  [5,] "Adrian" "Aracely" "Fernanda" "Jose" "Paty"  
##  [6,] "Adrian" "Aracely" "Fernanda" "Jose" "Ruby"  
##  [7,] "Adrian" "Aracely" "Fernanda" "Juan" "Laura" 
##  [8,] "Adrian" "Aracely" "Fernanda" "Juan" "Marcos"
##  [9,] "Adrian" "Aracely" "Fernanda" "Juan" "Oscar" 
## [10,] "Adrian" "Aracely" "Fernanda" "Juan" "Paty"
tail(combinations(n = n,r = grupos, S.personas),10)
##        [,1]    [,2]     [,3]     [,4]    [,5]  
## [243,] "Jose"  "Laura"  "Marcos" "Oscar" "Ruby"
## [244,] "Jose"  "Laura"  "Marcos" "Paty"  "Ruby"
## [245,] "Jose"  "Laura"  "Oscar"  "Paty"  "Ruby"
## [246,] "Jose"  "Marcos" "Oscar"  "Paty"  "Ruby"
## [247,] "Juan"  "Laura"  "Marcos" "Oscar" "Paty"
## [248,] "Juan"  "Laura"  "Marcos" "Oscar" "Ruby"
## [249,] "Juan"  "Laura"  "Marcos" "Paty"  "Ruby"
## [250,] "Juan"  "Laura"  "Oscar"  "Paty"  "Ruby"
## [251,] "Juan"  "Marcos" "Oscar"  "Paty"  "Ruby"
## [252,] "Laura" "Marcos" "Oscar"  "Paty"  "Ruby"

Combinaciones de 8

grupos <- 8
head(combinations(n = n,r = grupos, S.personas),10)
##       [,1]     [,2]      [,3]       [,4]   [,5]   [,6]     [,7]     [,8]   
##  [1,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Laura"  "Marcos" "Oscar"
##  [2,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Laura"  "Marcos" "Paty" 
##  [3,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Laura"  "Marcos" "Ruby" 
##  [4,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Laura"  "Oscar"  "Paty" 
##  [5,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Laura"  "Oscar"  "Ruby" 
##  [6,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Laura"  "Paty"   "Ruby" 
##  [7,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Marcos" "Oscar"  "Paty" 
##  [8,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Marcos" "Oscar"  "Ruby" 
##  [9,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Marcos" "Paty"   "Ruby" 
## [10,] "Adrian" "Aracely" "Fernanda" "Jose" "Juan" "Oscar"  "Paty"   "Ruby"
tail(combinations(n = n,r = grupos, S.personas),10)
##       [,1]       [,2]       [,3]   [,4]    [,5]     [,6]     [,7]    [,8]  
## [36,] "Adrian"   "Jose"     "Juan" "Laura" "Marcos" "Oscar"  "Paty"  "Ruby"
## [37,] "Aracely"  "Fernanda" "Jose" "Juan"  "Laura"  "Marcos" "Oscar" "Paty"
## [38,] "Aracely"  "Fernanda" "Jose" "Juan"  "Laura"  "Marcos" "Oscar" "Ruby"
## [39,] "Aracely"  "Fernanda" "Jose" "Juan"  "Laura"  "Marcos" "Paty"  "Ruby"
## [40,] "Aracely"  "Fernanda" "Jose" "Juan"  "Laura"  "Oscar"  "Paty"  "Ruby"
## [41,] "Aracely"  "Fernanda" "Jose" "Juan"  "Marcos" "Oscar"  "Paty"  "Ruby"
## [42,] "Aracely"  "Fernanda" "Jose" "Laura" "Marcos" "Oscar"  "Paty"  "Ruby"
## [43,] "Aracely"  "Fernanda" "Juan" "Laura" "Marcos" "Oscar"  "Paty"  "Ruby"
## [44,] "Aracely"  "Jose"     "Juan" "Laura" "Marcos" "Oscar"  "Paty"  "Ruby"
## [45,] "Fernanda" "Jose"     "Juan" "Laura" "Marcos" "Oscar"  "Paty"  "Ruby"

5. Interpretar el caso Permutaciones

  1. En permutaciones de 3
  2. ¿En cuántos casos sale el nombre de “Laura” en la primera posición? Ninguna.
  1. ¿Cuántas ocasiones aparece “Aracely” en segundo lugar? En 8 ocaciones.
  2. ¿Cuántas permutaciones se generan?
  1. En permutaciones de 5
  2. ¿En cuántos casos sale el nombre de “Laura” en la primera posición? Una
  1. ¿Cuántas ocasiones aparece “Aracely” en segundo lugar? 10
  2. ¿Cuántas permutaciones se generan?
  3. En permutaciones de 7
  4. ¿En cuántos casos sale el nombre de “Laura” en la primera posición? Ninguna
  5. ¿Cuántas ocasiones aparece “Aracely” en segundo lugar? 10
  6. ¿Cuántas permutaciones se generan?