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Multinomial coefficient

The multinomial coefficient[eq1]is used to denote the number of possible partitions of n objects into k groups having numerosity [eq2].

The coefficient takes its name from the following multinomial expansion:[eq3]where $n\in \U{2115} $ and the sum is over all the k-tuples [eq4] such that:[eq5]

Table of Contents


The number of possible ways to subdivide six objects into three groups of two objects each is given by the multinomial coefficient[eq6]

More details

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

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