\begin{definition}[Definition:Multinomial Coefficient]
Let $k_1, k_2, \ldots, k_m \in \Z_{\ge 0}$ be positive integers.
The '''multinomial coefficient''' of $k_1, \ldots, k_m$ is defined as:
:$\dbinom {k_1 + k_2 + \cdots + k_m} {k_1, k_2, \ldots, k_m} := \dfrac {\left({k_1 + k_2 + \cdots + k_m}\right)!} {k_1! \, k_2! \, \ldots k_m!}$
\end{definition}