# Roger Palay copyright 2016-02-15
# Saline, MI 48176
#
num_perm <- function( n, r )  # compute the number of permutations
{                             # of n things taken r at aa time
  if( r == 0 )                #  special case if r=0
    {return(1)}
  p <- 1                      # initialize the product
  for (i in 1:r)              # go throgh the r factors
  { p <- p*n
    n <- n-1
  }
  return(p)                   # send back the result
}

nPr <- function( n,r )
{ return (factorial(n)/factorial(n-r))}

num_comb <- function( n, r )
{ if( r == 0 ) {return(1)}
  if( r > n/2 ) { r <- n-r}
  return( num_perm(n,r)/num_perm(r,r))
}

nCr <- function(n,r )
{ return ( factorial(n)/factorial(n-r)/factorial(r))}