ILL 1971 Problem 54

A set $M$ is formed of $\binom{2n}{n}$ men, $n=1,2,\ldots$ . Prove that we can choose a subset $P$ of the set $M$ consisting of $n+1$ men such that one of the following conditions is satisfied: $(1)$ every member of the set $P$ knows every other member of the set $P$ ; $(2)$ no member of the set $P$ knows any other member of the set $P$ .