APMO 1989 Problem 4

Let $S$ be a set consisting of $m$ pairs $(a, b)$ of positive integers with the property that $1 \leq a<$ $b \leq n$. Show that there are at least

$$4 m \frac{\left(m-\frac{n^{2}}{4}\right)}{3 n}$$

triples $(a, b, c)$ such that $(a, b),(a, c)$, and $(b, c)$ belong to $S$.