The multinomial coefficientis used to denote the number of possible partitions of objects into groups having numerosity .

The coefficient takes its name from the following multinomial expansion:where and the sum is over all the -tuples such that:

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The number of possible ways to subdivide six objects into three groups of two objects each is given by the multinomial coefficient

The lecture entitled Partitions into groups provides an in-depth presentation of the multinomial coefficient.

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Please cite as:

Taboga, Marco (2021). "Multinomial coefficient", Lectures on probability theory and mathematical statistics. Kindle Direct Publishing. Online appendix. https://www.statlect.com/glossary/multinomial-coefficient.

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