Question

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

comb = calculate_combinations(n, r)

I need the number of possible combinations, not the actual combinations, so itertools.combinations does not interest me.

Finally, I want to avoid using factorials, as the numbers I’ll be calculating the combinations for can get too big and the factorials are going to be monstrous.

This seems like a REALLY easy to answer question, however I am being drowned in questions about generating all the actual combinations, which is not what I want.

Answer 1

Updated answer in 2023: Use the math.comb function, which exists since Python 3.8 and has gotten much faster in 3.11.

---

Old answer: See scipy.special.comb (scipy.misc.comb in older versions of scipy). When exact is False, it uses the gammaln function to obtain good precision without taking much time. In the exact case it returns an arbitrary-precision integer, which might take a long time to compute.