def nC(n, k=None, replacement=False):
    from sympy.functions.combinatorial.factorials import binomial
    from sympy.core.mul import prod

    if isinstance(n, SYMPY_INTS):
        if k is None:
            if not replacement:
                return 2**n
            return sum(nC(n, i, replacement) for i in range(n + 1))
        if k < 0:
            raise ValueError("k cannot be negative")
        if replacement:
            return binomial(n + k - 1, k)
        return binomial(n, k)
    if isinstance(n, _MultisetHistogram):
        N = n[_N]
        if k is None:
            if not replacement:
                return prod(m + 1 for m in n[_M])
            return sum(nC(n, i, replacement) for i in range(N + 1))
        elif replacement:
            return nC(n[_ITEMS], k, replacement)
        # assert k >= 0
        elif k in (1, N - 1):
            return n[_ITEMS]
        elif k in (0, N):
            return 1
        return _AOP_product(tuple(n[_M]))[k]
    else:
        return nC(_multiset_histogram(n), k, replacement)
Return the number of combinations of ``n`` items taken ``k`` at a time.
dataset/ETHPy150Open sympy/sympy/sympy/functions/combinatorial/numbers.py/nC