library(gtools)

nombres<-c("Manuel","Isaac","Pablo","Saul","Alejandra","Yander","Paty","Olga","Adriana","Mary")
nombres<-sort(nombres)
nombres
##  [1] "Adriana"   "Alejandra" "Isaac"     "Manuel"    "Mary"     
##  [6] "Olga"      "Pablo"     "Paty"      "Saul"      "Yander"
N<-length(nombres)
N
## [1] 10

Combinaciones

Grupos de dos

Com1<-combinations(N,2,nombres)
nrow(Com1)
## [1] 45
factorial(N)/(factorial(2)*factorial(N-2))
## [1] 45
head(Com1)
##      [,1]      [,2]       
## [1,] "Adriana" "Alejandra"
## [2,] "Adriana" "Isaac"    
## [3,] "Adriana" "Manuel"   
## [4,] "Adriana" "Mary"     
## [5,] "Adriana" "Olga"     
## [6,] "Adriana" "Pablo"

Grupos de cuatro

Com2<-combinations(N,4,nombres)
nrow(Com2)
## [1] 210
factorial(N)/(factorial(4)*factorial(N-4))
## [1] 210
head(Com2)
##      [,1]      [,2]        [,3]    [,4]    
## [1,] "Adriana" "Alejandra" "Isaac" "Manuel"
## [2,] "Adriana" "Alejandra" "Isaac" "Mary"  
## [3,] "Adriana" "Alejandra" "Isaac" "Olga"  
## [4,] "Adriana" "Alejandra" "Isaac" "Pablo" 
## [5,] "Adriana" "Alejandra" "Isaac" "Paty"  
## [6,] "Adriana" "Alejandra" "Isaac" "Saul"

Grupos de seis

Com3<-combinations(N,6,nombres)
nrow(Com3)
## [1] 210
factorial(N)/(factorial(6)*factorial(N-6))
## [1] 210
head(Com3)
##      [,1]      [,2]        [,3]    [,4]     [,5]   [,6]    
## [1,] "Adriana" "Alejandra" "Isaac" "Manuel" "Mary" "Olga"  
## [2,] "Adriana" "Alejandra" "Isaac" "Manuel" "Mary" "Pablo" 
## [3,] "Adriana" "Alejandra" "Isaac" "Manuel" "Mary" "Paty"  
## [4,] "Adriana" "Alejandra" "Isaac" "Manuel" "Mary" "Saul"  
## [5,] "Adriana" "Alejandra" "Isaac" "Manuel" "Mary" "Yander"
## [6,] "Adriana" "Alejandra" "Isaac" "Manuel" "Olga" "Pablo"

Permutaciones

Grupos de dos

Per1<-permutations(N,2,nombres)
nrow(Per1)
## [1] 90
factorial(N)/factorial(N-2)
## [1] 90
head(Per1)
##      [,1]      [,2]       
## [1,] "Adriana" "Alejandra"
## [2,] "Adriana" "Isaac"    
## [3,] "Adriana" "Manuel"   
## [4,] "Adriana" "Mary"     
## [5,] "Adriana" "Olga"     
## [6,] "Adriana" "Pablo"

Grupos de cuatro

Per2<-permutations(N,4,nombres)
nrow(Per2)
## [1] 5040
factorial(N)/factorial(N-4)
## [1] 5040
head(Per2)
##      [,1]      [,2]        [,3]    [,4]    
## [1,] "Adriana" "Alejandra" "Isaac" "Manuel"
## [2,] "Adriana" "Alejandra" "Isaac" "Mary"  
## [3,] "Adriana" "Alejandra" "Isaac" "Olga"  
## [4,] "Adriana" "Alejandra" "Isaac" "Pablo" 
## [5,] "Adriana" "Alejandra" "Isaac" "Paty"  
## [6,] "Adriana" "Alejandra" "Isaac" "Saul"

Grupos de seis

Per3<-permutations(N,6,nombres)
nrow(Per3)
## [1] 151200
factorial(N)/factorial(N-6)
## [1] 151200
head(Per3)
##      [,1]      [,2]        [,3]    [,4]     [,5]   [,6]    
## [1,] "Adriana" "Alejandra" "Isaac" "Manuel" "Mary" "Olga"  
## [2,] "Adriana" "Alejandra" "Isaac" "Manuel" "Mary" "Pablo" 
## [3,] "Adriana" "Alejandra" "Isaac" "Manuel" "Mary" "Paty"  
## [4,] "Adriana" "Alejandra" "Isaac" "Manuel" "Mary" "Saul"  
## [5,] "Adriana" "Alejandra" "Isaac" "Manuel" "Mary" "Yander"
## [6,] "Adriana" "Alejandra" "Isaac" "Manuel" "Olga" "Mary"

Combinaciones de grupo seis, Adriana esta en la primer columna

tail(Com3[which(Com3[,1]=='Adriana'),])
##        [,1]      [,2]   [,3]    [,4]    [,5]   [,6]    
## [121,] "Adriana" "Mary" "Olga"  "Pablo" "Paty" "Saul"  
## [122,] "Adriana" "Mary" "Olga"  "Pablo" "Paty" "Yander"
## [123,] "Adriana" "Mary" "Olga"  "Pablo" "Saul" "Yander"
## [124,] "Adriana" "Mary" "Olga"  "Paty"  "Saul" "Yander"
## [125,] "Adriana" "Mary" "Pablo" "Paty"  "Saul" "Yander"
## [126,] "Adriana" "Olga" "Pablo" "Paty"  "Saul" "Yander"

Combinaciones de grupo seis, Adriana en la primer o en la segunda o el la tercer columna

tail(Com3[which(Com3[,1]=='Adriana' | Com3[,2]=='Adriana' | Com3[,3]=='Adriana'),])
##        [,1]      [,2]   [,3]    [,4]    [,5]   [,6]    
## [121,] "Adriana" "Mary" "Olga"  "Pablo" "Paty" "Saul"  
## [122,] "Adriana" "Mary" "Olga"  "Pablo" "Paty" "Yander"
## [123,] "Adriana" "Mary" "Olga"  "Pablo" "Saul" "Yander"
## [124,] "Adriana" "Mary" "Olga"  "Paty"  "Saul" "Yander"
## [125,] "Adriana" "Mary" "Pablo" "Paty"  "Saul" "Yander"
## [126,] "Adriana" "Olga" "Pablo" "Paty"  "Saul" "Yander"

Combinaciones de grupo seis, Paty en la cuart o en la quinta o en la sexta columna

tail(Com3[which(Com3[,4]=='Paty' | Com3[,5]=='Paty' | Com3[,6]=='Paty'),])
##        [,1]     [,2]   [,3]    [,4]    [,5]   [,6]    
## [121,] "Manuel" "Mary" "Olga"  "Pablo" "Paty" "Saul"  
## [122,] "Manuel" "Mary" "Olga"  "Pablo" "Paty" "Yander"
## [123,] "Manuel" "Mary" "Olga"  "Paty"  "Saul" "Yander"
## [124,] "Manuel" "Mary" "Pablo" "Paty"  "Saul" "Yander"
## [125,] "Manuel" "Olga" "Pablo" "Paty"  "Saul" "Yander"
## [126,] "Mary"   "Olga" "Pablo" "Paty"  "Saul" "Yander"

Combinaciones de grupo de seis, Olga en la cuarta o en la quinta o en la sexta columna

tail(Com3[which(Com3[,4]=='Olga' | Com3[,5]=='Olga' | Com3[,6]=='Olga'),])
##       [,1]    [,2]     [,3]   [,4]   [,5]    [,6]    
## [76,] "Isaac" "Manuel" "Mary" "Olga" "Pablo" "Paty"  
## [77,] "Isaac" "Manuel" "Mary" "Olga" "Pablo" "Saul"  
## [78,] "Isaac" "Manuel" "Mary" "Olga" "Pablo" "Yander"
## [79,] "Isaac" "Manuel" "Mary" "Olga" "Paty"  "Saul"  
## [80,] "Isaac" "Manuel" "Mary" "Olga" "Paty"  "Yander"
## [81,] "Isaac" "Manuel" "Mary" "Olga" "Saul"  "Yander"

Combinaciones de grupo de seis, Olga en caulquiera de la seis columnas

tail(Com3[which(Com3[,1]=='Olga' | Com3[,2]=='Olga' | Com3[,3]=='Olga' | Com3[,4]=='Olga' | Com3[,5]=='Olga' | Com3[,6]=='Olga'),])
##        [,1]     [,2]   [,3]    [,4]    [,5]   [,6]    
## [121,] "Manuel" "Mary" "Olga"  "Pablo" "Paty" "Saul"  
## [122,] "Manuel" "Mary" "Olga"  "Pablo" "Paty" "Yander"
## [123,] "Manuel" "Mary" "Olga"  "Pablo" "Saul" "Yander"
## [124,] "Manuel" "Mary" "Olga"  "Paty"  "Saul" "Yander"
## [125,] "Manuel" "Olga" "Pablo" "Paty"  "Saul" "Yander"
## [126,] "Mary"   "Olga" "Pablo" "Paty"  "Saul" "Yander"

Combinaciones de grupo de seis, ‘Adriana’,‘Mary’,‘Olga’ y ‘Paty’ en cualquiera de las seis columnas

tail(Com3[which((Com3[,1]=='Olga' | Com3[,2]=='Olga' | Com3[,3]=='Olga' | Com3[,4]=='Olga' | Com3[,5]=='Olga' | Com3[,6]=='Olga') & (Com3[,1]=='Adriana' | Com3[,2]=='Adriana' | Com3[,3]=='Adriana' | Com3[,4]=='Adriana' | Com3[,5]=='Adriana' | Com3[,6]=='Adriana') & (Com3[,1]=='Mary' | Com3[,2]=='Mary' | Com3[,3]=='Mary' | Com3[,4]=='Mary' | Com3[,5]=='Mary' | Com3[,6]=='Mary') & (Com3[,1]=='Paty' | Com3[,2]=='Paty' | Com3[,3]=='Paty' | Com3[,4]=='Paty' | Com3[,5]=='Paty' | Com3[,6]=='Paty')),])
##       [,1]      [,2]     [,3]   [,4]    [,5]    [,6]    
## [10,] "Adriana" "Manuel" "Mary" "Olga"  "Pablo" "Paty"  
## [11,] "Adriana" "Manuel" "Mary" "Olga"  "Paty"  "Saul"  
## [12,] "Adriana" "Manuel" "Mary" "Olga"  "Paty"  "Yander"
## [13,] "Adriana" "Mary"   "Olga" "Pablo" "Paty"  "Saul"  
## [14,] "Adriana" "Mary"   "Olga" "Pablo" "Paty"  "Yander"
## [15,] "Adriana" "Mary"   "Olga" "Paty"  "Saul"  "Yander"

Permutaciones de grupo de seis, Adriana en la primer o segunda o tercer columna

tail(Per3[which(Per3[,1]=='Adriana' | Per3[,2]=='Adriana' | Per3[,3]=='Adriana'),])
##          [,1]     [,2]   [,3]      [,4]   [,5]    [,6]       
## [45355,] "Yander" "Saul" "Adriana" "Paty" "Olga"  "Pablo"    
## [45356,] "Yander" "Saul" "Adriana" "Paty" "Pablo" "Alejandra"
## [45357,] "Yander" "Saul" "Adriana" "Paty" "Pablo" "Isaac"    
## [45358,] "Yander" "Saul" "Adriana" "Paty" "Pablo" "Manuel"   
## [45359,] "Yander" "Saul" "Adriana" "Paty" "Pablo" "Mary"     
## [45360,] "Yander" "Saul" "Adriana" "Paty" "Pablo" "Olga"

Permutaciones de grupo de seis, Paty en la cuarta o quinta o sexta columna

tail(Per3[which(Per3[,4]=='Paty' | Per3[,5]=='Paty' | Per3[,6]=='Paty'),])
##          [,1]     [,2]   [,3]    [,4]   [,5]   [,6]       
## [45355,] "Yander" "Saul" "Pablo" "Paty" "Mary" "Olga"     
## [45356,] "Yander" "Saul" "Pablo" "Paty" "Olga" "Adriana"  
## [45357,] "Yander" "Saul" "Pablo" "Paty" "Olga" "Alejandra"
## [45358,] "Yander" "Saul" "Pablo" "Paty" "Olga" "Isaac"    
## [45359,] "Yander" "Saul" "Pablo" "Paty" "Olga" "Manuel"   
## [45360,] "Yander" "Saul" "Pablo" "Paty" "Olga" "Mary"

Permutaciones de grupo de seis, Olga en la cuarta o quinta o sexta columna

tail(Per3[which(Per3[,4]=='Olga' | Per3[,5]=='Olga' | Per3[,6]=='Olga'),])
##          [,1]     [,2]   [,3]   [,4]    [,5]   [,6]       
## [45355,] "Yander" "Saul" "Paty" "Pablo" "Mary" "Olga"     
## [45356,] "Yander" "Saul" "Paty" "Pablo" "Olga" "Adriana"  
## [45357,] "Yander" "Saul" "Paty" "Pablo" "Olga" "Alejandra"
## [45358,] "Yander" "Saul" "Paty" "Pablo" "Olga" "Isaac"    
## [45359,] "Yander" "Saul" "Paty" "Pablo" "Olga" "Manuel"   
## [45360,] "Yander" "Saul" "Paty" "Pablo" "Olga" "Mary"

Permutaciones de grupo de seis, Olga en cualquiera de las seis columnas

tail(Per3[which(Per3[,1]=='Olga' | Per3[,2]=='Olga' | Per3[,3]=='Olga' | Per3[,4]=='Olga' | Per3[,5]=='Olga' | Per3[,6]=='Olga'),])
##          [,1]     [,2]   [,3]   [,4]    [,5]   [,6]       
## [90715,] "Yander" "Saul" "Paty" "Pablo" "Mary" "Olga"     
## [90716,] "Yander" "Saul" "Paty" "Pablo" "Olga" "Adriana"  
## [90717,] "Yander" "Saul" "Paty" "Pablo" "Olga" "Alejandra"
## [90718,] "Yander" "Saul" "Paty" "Pablo" "Olga" "Isaac"    
## [90719,] "Yander" "Saul" "Paty" "Pablo" "Olga" "Manuel"   
## [90720,] "Yander" "Saul" "Paty" "Pablo" "Olga" "Mary"

Permutaciones de grupo de seis, Adriana, Mary, Olga y Paty en cualquiera de las seis columnas

tail(Per3[which((Per3[,1]=='Adriana' | Per3[,2]=='Adriana' | Per3[,3]=='Adriana' | Per3[,4]=='Adriana' | Per3[,5]=='Adriana' | Per3[,6]=='Adriana') & (Per3[,1]=='Mary' | Per3[,2]=='Mary' | Per3[,3]=='Mary' | Per3[,4]=='Mary' | Per3[,5]=='Mary' | Per3[,6]=='Mary') & (Per3[,1]=='Olga' | Per3[,2]=='Olga' | Per3[,3]=='Olga' | Per3[,4]=='Olga' | Per3[,5]=='Olga' | Per3[,6]=='Olga') & (Per3[,1]=='Paty' | Per3[,2]=='Paty' | Per3[,3]=='Paty' | Per3[,4]=='Paty' | Per3[,5]=='Paty' | Per3[,6]=='Paty')),])
##          [,1]     [,2]   [,3]   [,4]      [,5]      [,6]     
## [10795,] "Yander" "Saul" "Paty" "Adriana" "Mary"    "Olga"   
## [10796,] "Yander" "Saul" "Paty" "Adriana" "Olga"    "Mary"   
## [10797,] "Yander" "Saul" "Paty" "Mary"    "Adriana" "Olga"   
## [10798,] "Yander" "Saul" "Paty" "Mary"    "Olga"    "Adriana"
## [10799,] "Yander" "Saul" "Paty" "Olga"    "Adriana" "Mary"   
## [10800,] "Yander" "Saul" "Paty" "Olga"    "Mary"    "Adriana"

Permutaciones de grupo de seis, Adriana, Mary, Olga y Paty juntas, ya sea en las columnas 1-4, 2-5 o 3-6.

tail(Per3[which((Per3[,1]=='Adriana' & Per3[,2]=='Mary' & Per3[,3]=='Olga' & Per3[,4]=='Paty')| (Per3[,2]=='Adriana' & Per3[,3]=='Mary' & Per3[,4]=='Olga' & Per3[,5]=='Paty') | (Per3[,3]=='Adriana' & Per3[,4]=='Mary' & Per3[,5]=='Olga' & Per3[,6]=='Paty')),])
##       [,1]     [,2]        [,3]      [,4]   [,5]   [,6]  
## [85,] "Yander" "Adriana"   "Mary"    "Olga" "Paty" "Saul"
## [86,] "Yander" "Alejandra" "Adriana" "Mary" "Olga" "Paty"
## [87,] "Yander" "Isaac"     "Adriana" "Mary" "Olga" "Paty"
## [88,] "Yander" "Manuel"    "Adriana" "Mary" "Olga" "Paty"
## [89,] "Yander" "Pablo"     "Adriana" "Mary" "Olga" "Paty"
## [90,] "Yander" "Saul"      "Adriana" "Mary" "Olga" "Paty"