# Multinomial coefficient

From Encyclopedia of Mathematics

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.

#### References

[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: http://www.encyclopediaofmath.org/index.php?title=Multinomial_coefficient&oldid=18170

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098