The multinomial
coefficient![[eq1]](/images/multinomial_coefficient__1.png){kind=small}
is
used to denote the number of possible partitions of
objects into
groups having numerosity
![[eq2]](/images/multinomial_coefficient__4.png){kind=small}
.
The coefficient takes its name from the following multinomial
expansion:![[eq3]](/images/multinomial_coefficient__5.png){kind=small}
where
and the sum is over all the
-tuples
such
that:![[eq5]](/images/multinomial_coefficient__9.png){kind=small}
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]](/images/multinomial_coefficient__10.png)
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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