library(gtools)

nombres <- c("Keyla", "Stephanie", "Vanessa", "Aldo", "Eleazar", "Victor","Luis", "Manuel", "Mary", "Adriana", "Olga", "Paty")

nombres <- sort(nombres)

nombres

##  [1] "Adriana"   "Aldo"      "Eleazar"   "Keyla"     "Luis"      "Manuel"   
##  [7] "Mary"      "Olga"      "Paty"      "Stephanie" "Vanessa"   "Victor"

N <- length(nombres) 
n <- 6 

permutaciones <- permutations(N, n, nombres)

head(permutaciones)

##      [,1]      [,2]   [,3]      [,4]    [,5]   [,6]       
## [1,] "Adriana" "Aldo" "Eleazar" "Keyla" "Luis" "Manuel"   
## [2,] "Adriana" "Aldo" "Eleazar" "Keyla" "Luis" "Mary"     
## [3,] "Adriana" "Aldo" "Eleazar" "Keyla" "Luis" "Olga"     
## [4,] "Adriana" "Aldo" "Eleazar" "Keyla" "Luis" "Paty"     
## [5,] "Adriana" "Aldo" "Eleazar" "Keyla" "Luis" "Stephanie"
## [6,] "Adriana" "Aldo" "Eleazar" "Keyla" "Luis" "Vanessa"

PREGUNTA 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" "Aldo" "Eleazar" "Keyla" "Luis"   "Olga"  
## [2,] "Adriana" "Aldo" "Eleazar" "Keyla" "Manuel" "Olga"  
## [3,] "Adriana" "Aldo" "Eleazar" "Keyla" "Mary"   "Olga"  
## [4,] "Adriana" "Aldo" "Eleazar" "Keyla" "Olga"   "Luis"  
## [5,] "Adriana" "Aldo" "Eleazar" "Keyla" "Olga"   "Manuel"
## [6,] "Adriana" "Aldo" "Eleazar" "Keyla" "Olga"   "Mary"

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]     
## [332635,] "Victor" "Vanessa" "Stephanie" "Paty" "Olga" "Aldo"   
## [332636,] "Victor" "Vanessa" "Stephanie" "Paty" "Olga" "Eleazar"
## [332637,] "Victor" "Vanessa" "Stephanie" "Paty" "Olga" "Keyla"  
## [332638,] "Victor" "Vanessa" "Stephanie" "Paty" "Olga" "Luis"   
## [332639,] "Victor" "Vanessa" "Stephanie" "Paty" "Olga" "Manuel" 
## [332640,] "Victor" "Vanessa" "Stephanie" "Paty" "Olga" "Mary"

PREGUNTA 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' | permutaciones[,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" "Aldo" "Eleazar" "Mary" "Olga" "Paty"
## [2,] "Adriana" "Aldo" "Eleazar" "Mary" "Paty" "Olga"
## [3,] "Adriana" "Aldo" "Eleazar" "Olga" "Mary" "Paty"
## [4,] "Adriana" "Aldo" "Eleazar" "Olga" "Paty" "Mary"
## [5,] "Adriana" "Aldo" "Eleazar" "Paty" "Mary" "Olga"
## [6,] "Adriana" "Aldo" "Eleazar" "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' | permutaciones[,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]     
## [20155,] "Victor" "Vanessa" "Paty" "Adriana" "Mary"    "Olga"   
## [20156,] "Victor" "Vanessa" "Paty" "Adriana" "Olga"    "Mary"   
## [20157,] "Victor" "Vanessa" "Paty" "Mary"    "Adriana" "Olga"   
## [20158,] "Victor" "Vanessa" "Paty" "Mary"    "Olga"    "Adriana"
## [20159,] "Victor" "Vanessa" "Paty" "Olga"    "Adriana" "Mary"   
## [20160,] "Victor" "Vanessa" "Paty" "Olga"    "Mary"    "Adriana"