Pair-cover bound for a two-intersecting uniform family
= Pair-cover bound for a two-intersecting uniform family
Fix a member of size $r$. Every other member of a <two-intersecting family> contains a pair from that fixed member. Counting all $r$-sets containing these pairs gives $|\mathcal F|\leq\binom r2\binom{n-2}{r-2}$ for a <uniform set family>.