comb

comb(N, k, exact=False, repetition=False)

The number of combinations of N things taken k at a time.

This is often expressed as “N choose k”.

When exact=False, the result is approximately and efficiently computed using the following formula:

\[\exp\left\{\ln{\Gamma(N+1)} - [\ln{\Gamma(k+1)} + \ln{\Gamma(N+1-k)}]\right\}\]

using the Gamma function.

Parameters:

• N (np.ndarray) – The number of things.

• k (np.ndarray) – The number of elements taken.

• exact (bool, optional) – If True, the result is computed exactly and returned as an integer type. Currently, vectorization is not supported for exact=True.

• repetition (bool, optional) – If repetition is True, then the number of combinations with repetition is computed.

Returns:

comb – The number of combinations of N things taken k at a time.

Return type:

np.ndarray