Multinomial coefficient

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The coefficient

of in the expansion of the polynomial . In combinatorics, the multinomial coefficient expresses the following: a) the number of possible permutations of elements of which are of one form, of another form of the -th form; b) the number of ways of locating different elements in different cells in which cell contains elements, , without taking the order of the elements in any cell into account.

Particular cases of multinomial coefficients are the binomial coefficients.


[1] M. Hall, "Combinatorial theory" , Wiley (1986)
[2] J. Riordan, "An introduction to combinatorial analysis" , Wiley (1967)
How to Cite This Entry:
Multinomial coefficient. S.A. Rukova (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098