  Given two integers $k\geq 2$ and $a>1$, let $N_k(a)$ stand for the number of
multinomial coefficients, with $k$ terms, equal to $a$. We study the behavior
of $N_k(a)$ and show that its average and normal orders are equal to $k(k-1)$.
We also prove that $N_k(a)=O\left((\log a/\log\log a)^{k-1}\right)$ and make
several propositions about extreme results regarding large values of $N_k(a)$.
