UPSC Prelims 2015·CSAT·Quantitative Aptitude·Combinatorics and Probability

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

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Last updated 23 May 2026, 3:31 pm IST
  1. A4
  2. B12
  3. C18
  4. DNone of the aboveCorrect

Explanation

To find the number of possible combinations, we must consider the two scenarios based on which candidate is selected as the Principal. First, identify the candidates. There are 6 total candidates. Let us call the two candidates eligible for Principal A and B. The other four candidates are C, D, E, and F. Scenario 1: Candidate A is selected as Principal. Since A is selected, there are 5 remaining candidates (B, C, D, E, and F) who are all eligible for the 2 Vice-Principal posts. The number of ways to choose 2 people from 5 is 10. Scenario 2: Candidate B is selected as Principal. Since B is selected, there are 5 remaining candidates (A, C, D, E, and F) who are all eligible for the 2 Vice-Principal posts. The number of ways to choose 2 people from 5 is 10. Total combinations: Adding the two scenarios together, we get 10 plus 10, which equals 20. Since 20 is not among the options A (4), B (12), or C (18), the correct answer is D (None of the above).
Quantitative Aptitude: A selection is to be made for one post of Principal and two posts of Vice-Principal. Amongst the six candidates called f
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