#Python 3, 109

<!-- language-all: lang-python -->

    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