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

If you really only need the case where n is much larger than p, one way to go would be to use the Stirling's formula for the factorials. (if n>>1 and p is order one, Stirling approximate n! and (n-p)!, keep p! as it is etc.)