[Solved] Fast algorithm to calculate n! / (q!)^r

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I think it’s a very bad idea to calculate two very large numbers and hope that the quotient comes out as something sensible.

Start by taking the natural log:

ln(n!/(q!)^r) = ln(n!) - r*ln(q!)

You can use gammaln() for the two function values, simplify, then take exp() to get the result you want:

value = exp(gammln(n+1) -r*gammln(q+1))

Numerical Recipes has a nice chapter on how to implement functions like gammln().

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solved Fast algorithm to calculate n! / (q!)^r