Multinomial Count

Problem

Count the distinct orderings of a multiset described by its item counts.

The multinomial count is n! / (c_1! * c_2! * ...) where n = sum(counts). Return 0 if any count is negative and 1 for an empty list.

Hint

Divide n! by the factorial of each repeated count.

case 1

in: [[2,1]]

expected: 3

case 2

in: [[1,1,1]]

expected: 6

case 3

in: [[3,0]]

expected: 1

case 4

in: [[2,2,2]]

expected: 90

case 5

in: [[]]

expected: 1

Starter codePython

import math


def multinomial_count(counts):
    # Your code here
    pass

5 test cases · run your code against them in the editor