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
- (a) 4
- (b) 12
- (c) 18
- (d) None of the above ✓ UPSC's answer
Why the answer is (d)
• The Principal can be chosen only from the 2 eligible candidates: 2 ways.
• The two Vice-Principals are then chosen from the remaining 5 candidates: 5C2 = 10 ways.
• Total selections = 2 × 10 = 20.
• 20 is not among 4, 12 or 18, so the answer is ‘None of the above’ — option (d).
• Hence option (d).
Why the other options are wrong
- (a) 4
- The count is 2 × 10 = 20, not 4.
- (b) 12
- The count is 20, not 12.
- (c) 18
- The count is 20, not 18.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.