SMO 2004 Problem 1

Let $m,n$ be integers so that $m \ge n > 1$ . Let $F_1,...,F_k$ be a collection of $n$ -element subsets of $\{1,...,m\}$ so that $F_i\cap F_j$ contains at most $1$ element, $1 \le i < j \le k$ . Show that $k\le \frac{m(m-1)}{n(n-1)}$