Multinomial coefficient

Remarks

For $m = 2$ it is the binomial coefficient: $\binom{n}{k, n-k} = \binom{n}{k}$. It counts the ways to put $n$ distinct objects into $m$ labelled boxes, with $k_i$ objects in box $i$. It also counts the distinct words that use a letter $a_i$ exactly $k_i$ times. For example, MISSISSIPPI has $\frac{11!}{1!\,4!\,4!\,2!} = 34650$ distinct rearrangements. It is the coefficient in the multinomial theorem.