Problem
COM-B1-M12-P009 Set 3. Clubs
#9
★★☆☆☆ Level 2 of 5
Each of \(15\) students attends exactly \(2\) clubs. Each club has exactly \(5\) students. How many clubs are there?
Count pairs “student, club”.
Counting by students gives \(15\cdot2=30\) pairs. If there are \(k\) clubs, counting by clubs gives \(5k\). Thus \(5k=30\), so \(k=6\).
Double counting.