In a school, there are $m$ teachers and $n$ students. We assume that each teacher has exactly $k$ students, and each student has exactly $\ell$ teachers. Determine a relation between $m, n, k, \ell$.
Let $X$ be the number of pairs $(e, p)$ where $e$ is a student of $p$. Then we have $|X|=m k=n \ell$.