# Let $S$ be the set of all subsets of $\{1,…,n\}$ with size $k$. Find the number of other elements that has an intersection of size $l$ with a vertex

Let $S$ be the set of subsets of size $k$ from $\{1,\dots,n\}$.

Let $a$ be an element of $S$.

Determine the number of other elements of $S$ that have an intersection of size $l$ with $a$.