Let $X$ and $Y$ be disjoint sets containing $p$ and $q$ elements respectively, and let the set $Z$ be defined as $Z\bigcup Y$. Find the number of subsets $S$ of $Z$ that contains $m$ elements and also has the property that $S\bigcap X$ has $n$ elements.
What I've tried is:
Total elements in $Z$ is $p+q$, so subsets containing $m$ elements is $C(p+q,m)m!$ where $C$ denotes combination.
How to include $n $ elements interesection ?