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Stars-and-Bars Multiset Coefficient Calculator

Number of ways to put k indistinguishable balls into n distinct bins.

Compute the multiset coefficient C(n + k − 1, k) — the number of ways to distribute k indistinguishable items into n distinguishable bins (a.k.a. the stars-and-bars count).

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

C(n + k − 1, k) = (n + k − 1)! / (k! · (n − 1)!)

In depth

Compute the multiset coefficient C(n + k − 1, k) — the number of ways to distribute k indistinguishable items into n distinguishable bins (a.k.a. the stars-and-bars count).