UPSC Prelims 2003 · General Studies
Question 69: Basic Numeracy
A two-member committee comprising of one male and one female member is to be constituted out of five males and three females. Amongst the females, Ms. A refuses to be a member of the committee in which Mr. B is taken as the member. In how many different ways can the committee be constituted?
AnswerThe answer is (d).
Without any restriction, one male and one female can be chosen in 5 x 3 = 15 ways. Ms A refuses to serve with Mr B, so remove the one pair that has Ms A and Mr B together: 15 - 1 = 14. Every other pair is allowed, including Ms A with the other four men. Remember: total ways minus the forbidden combination.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
This follows an unofficial answer: UPSC has not published its key for this year, and if that answer is wrong, so is this path.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) 11 would exclude four pairs; only one is barred.
- (b) 12 would exclude three pairs; only one is barred.
- (c) 13 would exclude two pairs; only one is barred.
- (d) Correct: 15 - 1 = 14.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2003, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.