The following program calculates nCr in an efficient manner (compared to calculating factorials etc.)
import operator as op
from functools import reduce
def ncr(n, r):
r = min(r, n-r)
numer = reduce(op.mul, range(n, n-r, -1), 1)
denom = reduce(op.mul, range(1, r+1), 1)
return numer // denom # or / in Python 2
As of Python 3.8, binomial coefficients are available in the standard library as math.comb:
>>> from math import comb
>>> comb(10,3)
120