information:extraction, structural:reformatting, structural:summarization, stylistic:style_transfer
Generalization to multinomials

Binomial coefficients can be generalized to multinomial coefficients defined to be the number:

where

While the binomial coefficients represent the coefficients of (x + y), the multinomial coefficientsrepresent the coefficients of the polynomial

The case r = 2 gives binomial coefficients:

The combinatorial interpretation of multinomial coefficients is distribution of n distinguishable elements over r (distinguishable) containers, each containing exactly k elements, where i is the index of the container.

Multinomial coefficients have many properties similar to those of binomial coefficients, for example the recurrence relation:

and symmetry:

where (σ i) {\displaystyle (\sigma _{i})} is a permutation of (1, 2,..., r).