Statistics: combinations in Python

Question

I need to compute combinatorials (nCr) in Python but cannot find the function to do that in math, numpy or stat libraries. Something

Answer 1

A literal translation of the mathematical definition is quite adequate in a lot of cases (remembering that Python will automatically use big number arithmetic):

from math import factorial

def calculate_combinations(n, r):
    return factorial(n) // factorial(r) // factorial(n-r)

For some inputs I tested (e.g. n=1000 r=500) this was more than 10 times faster than the one liner reduce suggested in another (currently highest voted) answer. On the other hand, it is out-performed by the snippit provided by @J.F. Sebastian.