Topic links: https://codeforces.com/contest/1312
\[ \begin{align} &C_{p-1}^{x}*C_{x}^{1}*C_{p-1-x}^{y-1} \nonumber \\ &=\frac{(p-1)!}{(p-1-x)!x!}*x*\frac{(p-1-x)!}{(p-1-x-(y-1))!(y-1)!} \nonumber \\ &=\frac{(p-1)!}{(p-n+1)!(x-1)!(y-1)!} \nonumber \\ \end{align} \]