222. If $\ a^{p} x^{q}$ is one of the terms in the expansion of $(a+x)^{n}$, what condition do $p$ and $q$ satisfy? What is the coefficient $M$?
222. $p+q=n ; M=C_{p+q}^{p}=C_{p+q}^{q}=\binom{n}{p}=\frac{n!}{p!(n-p)!}=$

$$
=\frac{1 \cdot 2 \cdot 3 \ldots n}{1 \cdot 2 \cdot 3 \ldots p \cdot 1 \cdot 2 \cdot 3 \ldots(n-p)}=\frac{n(n-1)(n-2) \ldots(n-p+1)}{1 \cdot 2 \cdot 3 \ldots p}
$$