Let $D$ be a family of $s$-element subsets of $\{1.\ldots,n\}$ such that every $k$ members of $D$ have non-empty intersection. Denote by $D(n,s,k)$ the maximum cardinality of such a family. a) Find $D(n,s,4)$. b) Find $D(n,s,3)$.
Problem
Source: Iranian National Olympiad (3rd Round) 2006
Tags: combinatorics proposed, combinatorics