Problem
COM-B1-M11-P014 Clubs
#14
★★★☆☆ Level 3 of 5
In a school, \(12\) students attend clubs. Each student attends exactly \(3\) clubs, and each club has exactly \(4\) students. How many clubs are there?
Count pairs “student, club”.
Counting pairs \((student, club)\) by students gives \(12\cdot3=36\). If there are \(k\) clubs, counting by clubs gives \(4k\). Hence \(4k=36\), so \(k=9\).
Pure double counting.