On Factorial, Permutation and Combination

R Functions: Factorial, Permutation, Combination

## Function: Factorial of a Number
## Input: A non-negative integer
## Ouput: A positive integer

Factorial <- function(N){
    if(N==0) return(1)
    else return(N*Factorial(N-1))
}

## Function: Permutation 
## Input: Positive Integer N and integer k such that
##          k >= 0 and k < n.
## Output: A positive integer

Permutation <- function(N,k){
    return(Factorial(N)/Factorial(N-k))
}

## Function: Combination 
## Input: A positive integer N and an integer k
##          such that k >= 0 and k < N.
## Output: A positive integer 
Combination <- function(N,k){
    return(Permutation(N,k)/Factorial(k))
}

Examples:

Factorial(0)

## [1] 1

Factorial(1)

## [1] 1

Factorial(2)

## [1] 2

Factorial(10)

## [1] 3628800

Permutation(5,0)

## [1] 1

Permutation(5,2)

## [1] 20

Permutation(5,5)

## [1] 120

Permutation(20,10)

## [1] 670442572800

Combination(5,0)

## [1] 1

Combination(5,5)

## [1] 1

Combination(20,10)

## [1] 184756