chickadee » math » multinomial

n

integer

ks

(list-of integer)

A generalization of binomial to multiple sets of choices; e.g. (multinomial n (list k0 k1 k2)) is the number of ways to choose a set of k0 items, a set of k1 items, and a set of k2 items from a set of n items. All arguments must be nonnegative.

When (apply + ks) = n, this is equivalent to (apply / (factorial n) (map factorial ks)). Otherwise, multinomial returns 0.

> (multinomial 5 '(3 2))
10
> (= (multinomial 8 '(5 3))
     (binomial 8 5)
     (binomial 8 3))
#t
> (multinomial 10 '(5 3 2))
2520
> (multinomial 0 '())
1
> (multinomial 4 '(1 1))
0

Wikipedia: Multinomial Coefficient