ength of
:func:`distinct_permutations`.  For example, there are 83,160 distinct
anagrams of the word "abracadabra":

    >>> from more_itertools import distinct_permutations, ilen
    >>> ilen(distinct_permutations('abracadabra'))
    83160

This can be computed directly from the letter counts, 5a 2b 2r 1c 1d:

    >>> from collections import Counter
    >>> list(Counter('abracadabra').values())
    [5, 2, 2, 1, 1]
    >>> multinomial(5, 2, 1, 1, 2)
    83160

A binomial coefficient is a special case of multinomial where there are
only two categories.  For example, the number of ways to arrange 12 balls
with 5 reds and 7 blues is ``multinomial(5, 7)`` or ``math.comb(12, 5)``.

When the multiplicities are all just 1, :func:`multinomial`
is a special case of ``math.factorial`` so that
``multinomial(1, 1, 1, 1, 1, 1, 1) == math.factorial(7)``.

Reference:  https://en.wikipedia.org/wiki/Multinomial_theorem

)