UPSC Prelims 2006 · General Studies
Question 102: Basic Numeracy
A mixed doubles tennis game is to be played between two teams (each team consists of one male and one female). There are 4 married couples. No team is to consist of a husband and his wife. What is the maximum number of games that can be played?
AnswerThe answer is (d).
A team is a man and a woman who are not married to each other: 4 men x 3 wives other than their own = 12 possible teams. A game needs two teams with no player in common. Pairs of teams: C(12,2) = 66. Remove pairs sharing the same man: 4 men x C(3,2) = 12. Remove pairs sharing the same woman: 12. That leaves 66 - 12 - 12 = 42 games.
Why each option is right or wrong
- (a) 12 is only the number of possible teams.
- (b) 21 is half of the correct count.
- (c) 36 does not follow from the count.
- (d) Correct: 66 - 12 - 12 = 42 games.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2006, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.