In a school, there are $m$ teachers and $n$ students. We assume that each teacher has exactly $k$ students, and that a student always has exactly $l$ teachers. Determine a relation between $m, n, k, l$.
We count the pairs $(p, e)$ where $p$ is a teacher, $e$ is a student, and $p$ is a teacher of $e$. There are $m$ choices for $p$, and then $k$ choices for one of their students, so there are $p k$ possible pairs. But we can count this differently: there are $n$ choices for $e$, and then $l$ choices for one of their teachers, so there are $n l$ possible pairs. Thus, $n l = k m$.