Problem
COM-B1-M04-P020 Committees and Members
#20
★★★☆☆ Level 3 of 5
There are \(12\) committees, each with \(5\) people, and \(20\) people total participate. Prove that some person belongs to at least \(3\) committees.
Count pairs \((person,committee)\).
Total memberships: \(12\cdot5=60\). The average number of committees per person is \(60/20=3\). Hence some person belongs to at least \(3\) committees.
Existence via average.