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Python 3, 109 103

from functools import*
from math import*
def g(n,k):
    for i in k:r//=f(i)
    return r

n as integer, k as iterable.


import functools #recude
import math #factorial
import operator #mul
def multinomial(n, k):
    numerator = math.factorial(n)
    denominator = functools.reduce(operator.mul, (math.factorial(i) for i in k)) #product of iterable k
    return numerator//denominator