Fastest way to generate binomial coefficients

Question

I need to calculate combinations for a number.

What is the fastest way to calculate nCp where n>>p?

I need a fast way to generate binomial coefficients for a

Answer 1

nCp = n! / ( p! (n-p)! ) =
      ( n * (n-1) * (n-2) * ... * (n - p) * (n - p - 1) * ... * 1 ) /
      ( p * (p-1) * ... * 1     * (n - p) * (n - p - 1) * ... * 1 )

If we prune the same terms of the numerator and the denominator, we are left with minimal multiplication required. We can write a function in C to perform 2p multiplications and 1 division to get nCp:

int binom ( int p, int n ) {
    if ( p == 0 ) return 1;
    int num = n;
    int den = p;
    while ( p > 1 ) {
        p--;
        num *= n - p;
        den *= p;
    }
    return num / den;
}