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