Práctica No. 6 Combinaciones y Permutaciones mediante R

library(gtools)

nombres <- c( "Adriana", "Mary", "Olga" , "Paty", "Ivan","Luis","Aldo","Keyla","Manuel","Vanessa","estefany","Eleazar")
nombres <- sort(nombres)
nombres

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

N<- length(nombres)
n<- 2
combinaciones<- combinations(N,n,nombres)
head(combinaciones)

##      [,1]      [,2]      
## [1,] "Adriana" "Aldo"    
## [2,] "Adriana" "Eleazar" 
## [3,] "Adriana" "estefany"
## [4,] "Adriana" "Ivan"    
## [5,] "Adriana" "Keyla"   
## [6,] "Adriana" "Luis"

nrow(combinaciones)

## [1] 66

factorial(N)/(factorial(n)*(factorial(N-n)))

## [1] 66

N<- length(nombres)
n<- 4
combinaciones<- combinations(N,n,nombres)
head(combinaciones)

##      [,1]      [,2]   [,3]      [,4]      
## [1,] "Adriana" "Aldo" "Eleazar" "estefany"
## [2,] "Adriana" "Aldo" "Eleazar" "Ivan"    
## [3,] "Adriana" "Aldo" "Eleazar" "Keyla"   
## [4,] "Adriana" "Aldo" "Eleazar" "Luis"    
## [5,] "Adriana" "Aldo" "Eleazar" "Manuel"  
## [6,] "Adriana" "Aldo" "Eleazar" "Mary"

nrow(combinaciones)

## [1] 495

factorial(N)/(factorial(n)*(factorial(N-n)))

## [1] 495

N<- length(nombres)
n<- 6
combinaciones<- combinations(N,n,nombres)
head(combinaciones)

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

nrow(combinaciones)

## [1] 924

factorial(N)/(factorial(n)*(factorial(N-n)))

## [1] 924

N <- length(nombres)
n<- 2
permutaciones <- permutations(N,n,nombres)
head(permutaciones)

##      [,1]      [,2]      
## [1,] "Adriana" "Aldo"    
## [2,] "Adriana" "Eleazar" 
## [3,] "Adriana" "estefany"
## [4,] "Adriana" "Ivan"    
## [5,] "Adriana" "Keyla"   
## [6,] "Adriana" "Luis"

nrow(permutaciones)

## [1] 132

factorial(N) / (factorial (N-n))

## [1] 132

N <- length(nombres)
n<- 4
permutaciones <- permutations(N,n,nombres)
head(permutaciones)

##      [,1]      [,2]   [,3]      [,4]      
## [1,] "Adriana" "Aldo" "Eleazar" "estefany"
## [2,] "Adriana" "Aldo" "Eleazar" "Ivan"    
## [3,] "Adriana" "Aldo" "Eleazar" "Keyla"   
## [4,] "Adriana" "Aldo" "Eleazar" "Luis"    
## [5,] "Adriana" "Aldo" "Eleazar" "Manuel"  
## [6,] "Adriana" "Aldo" "Eleazar" "Mary"

nrow(permutaciones)

## [1] 11880

factorial(N) / (factorial (N-n))

## [1] 11880

N <- length(nombres)
n<- 6
permutaciones <- permutations(N,n,nombres)
head(permutaciones)

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

nrow(permutaciones)

## [1] 665280

factorial(N) / (factorial (N-n))

## [1] 665280

###pregunta numero 12.-

head(permutaciones[which(permutaciones[,4] == 'Olga' | permutaciones[,5] == 'Olga' | permutaciones[,6] == 'Olga'),])

##      [,1]      [,2]   [,3]      [,4]       [,5]     [,6]  
## [1,] "Adriana" "Aldo" "Eleazar" "estefany" "Ivan"   "Olga"
## [2,] "Adriana" "Aldo" "Eleazar" "estefany" "Keyla"  "Olga"
## [3,] "Adriana" "Aldo" "Eleazar" "estefany" "Luis"   "Olga"
## [4,] "Adriana" "Aldo" "Eleazar" "estefany" "Manuel" "Olga"
## [5,] "Adriana" "Aldo" "Eleazar" "estefany" "Mary"   "Olga"
## [6,] "Adriana" "Aldo" "Eleazar" "estefany" "Olga"   "Ivan"

tail(permutaciones[which(permutaciones[,4] == 'Olga' | permutaciones[,5] == 'Olga' | permutaciones[,6] == 'Olga'),])

##           [,1]      [,2]   [,3]   [,4]   [,5]     [,6]      
## [166315,] "Vanessa" "Paty" "Mary" "Olga" "Manuel" "Aldo"    
## [166316,] "Vanessa" "Paty" "Mary" "Olga" "Manuel" "Eleazar" 
## [166317,] "Vanessa" "Paty" "Mary" "Olga" "Manuel" "estefany"
## [166318,] "Vanessa" "Paty" "Mary" "Olga" "Manuel" "Ivan"    
## [166319,] "Vanessa" "Paty" "Mary" "Olga" "Manuel" "Keyla"   
## [166320,] "Vanessa" "Paty" "Mary" "Olga" "Manuel" "Luis"

###pregunta 13-.

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

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,] "Vanessa" "Paty" "Olga" "Mary" "Manuel" "Aldo"    
## [332636,] "Vanessa" "Paty" "Olga" "Mary" "Manuel" "Eleazar" 
## [332637,] "Vanessa" "Paty" "Olga" "Mary" "Manuel" "estefany"
## [332638,] "Vanessa" "Paty" "Olga" "Mary" "Manuel" "Ivan"    
## [332639,] "Vanessa" "Paty" "Olga" "Mary" "Manuel" "Keyla"   
## [332640,] "Vanessa" "Paty" "Olga" "Mary" "Manuel" "Luis"