UPSC Prelims 2015 · CSAT
Question 48: Basic Numeracy
A selection is to be made for one post of Principal and two posts of Vice-Principal. Amongst the six candidates called for the interview, only two are eligible for the post of Principal while they all are eligible for the post of Vice-Principal. The number of possible combinations of selectees is
AnswerUPSC’s answer is (d).
Choose the Principal first, since only two candidates are eligible: 2 ways. The two Vice-Principals are then chosen from the remaining 5 candidates, all eligible, in 5C2 = (5 × 4) ÷ 2 = 10 ways. Total selections = 2 × 10 = 20. This matches none of 4, 12 or 18, so the answer is 'none of the above'.
Why each option is right or wrong
- (a) Wrong: 4 is far below the 20 selections possible.
- (b) Wrong: 12 is below the 20 possible.
- (c) Wrong: 18 is not the count; 2 × 10 = 20.
- (d) Right: the count is 20, which is not among the options.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2015, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.