Q115
ArithmeticPermutations, Combinations & Probability
How many members should at least be there in a Club so that it is guaranteed that at least two members have the same month of birth?
- a.3
- b.12
- c.13
- d.24
Answer: (C) 13
This is the pigeonhole principle: with 12 months (pigeonholes), 12 members could all have different birth months, but a 13th member must share a month with someone. So the minimum that guarantees a match is $12 + 1 = 13$. Option B (12) is the largest group that can still avoid a match, and option D (24) is a distractor based on 'two per month'. Extension often asked: to guarantee that at least three members share a birth month you need $2 \times 12 + 1 = 25$; to guarantee two people with the same birthday you need 367 people.