UPSC Prelims 2003 Q69: Science & Technology – Quantitative Aptitude
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?
- (a) 11
- (b) 12
- (c) 13
- (d) 14
Answer: (d) 14
Explanation
Forming a two-member committee with a restriction
| Step | Count |
|---|---|
| Without the restriction | 5 males x 3 females = 15 committees |
| Committees with both Ms A and Mr B | 1 |
| With the restriction | 15 - 1 = 14 |
There are 5 x 3 = 15 possible committees, and the one with both Ms A and Mr B is not allowed, so 14 committees can be formed.
Answer: (d) 14.
Why each option is right or wrong
- (a) Incorrect. 11 removes too many committees.
- (b) Incorrect. 12 removes too many committees.
- (c) Incorrect. 13 removes two committees, not one.
- (d) CORRECT. 15 - 1 = 14 committees.
Key point
Total pairs minus the forbidden pair.
Remember
5 x 3 - 1 = 14 committees.
Common mistakes
- Removing all committees that include Ms A.
- Removing all committees that include Mr B.
- Using 5 + 3 instead of 5 x 3 pairs.
Exam tip
Only the pair (Ms A, Mr B) is forbidden.
Sources
- NCERT Class XI Mathematics — Permutations and Combinations
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Permutations and Combinations)