for questions about multinomial coefficients

Multinomial coefficients are the coefficients arising in the expansion of:

$$(a_1+\dots+a_k)^n$$

and take the form:

$$\binom{n}{m_1,\dots,m_k}=\frac{n!}{m_1!\dots m_k!}$$

where:

$$\sum_{i=1}^k m_i = n$$