Question 4
Let $S$ be a set consisting of $m$ pairs $(a,b)$ of positive integers with $1\le a\lt b\le n$. Show that there are at least
$$\frac{4m\left(m-\frac{n^2}{4}\right)}{3n}$$
triples $(a,b,c)$ such that $(a,b),(a,c),(b,c)$ belong to $S$.
$$\frac{4m\left(m-\frac{n^2}{4}\right)}{3n}$$
triples $(a,b,c)$ such that $(a,b),(a,c),(b,c)$ belong to $S$.