Multinomial Coefficient Calculator

About this calculator

The multinomial coefficient generalizes the binomial coefficient to more than two groups, counting the number of ways to arrange n items when they're split into groups of sizes k₁, k₂, … (with k₁+k₂+…=n) and items within each group are identical: n! / (k₁!·k₂!·…·kᵣ!).

Combinatorics and probability students use it to count arrangements like the distinct letter-orderings of a word with repeated letters, statisticians use it as the core term in the multinomial probability distribution (an extension of the binomial to more than two outcomes), and computer scientists use it in problems involving anagrams or partitioning items into labeled groups.