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Multinomial Coefficient for Three Groups Calculator

n!/(n₁!n₂!n₃!) — arrangements with three categories.

Calculates the multinomial coefficient n!/(n₁!·n₂!·n₃!) and the probability of each outcome when items are drawn from a population with three categories.

Priya Venkatesan By Priya Venkatesan
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

M = n! / (n₁! · n₂! · n₃!)

In depth

Calculates the multinomial coefficient n!/(n₁!·n₂!·n₃!) and the probability of each outcome when items are drawn from a population with three categories.