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Python 3, 109

from functools import*
from math import*
f=factorial
lambda n,k:f(n)//reduce(lambda x,y:x*y,(f(i)for i in k))

n as integer, k as iterable.

Ungolfed:

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