A selection is to be made for one post of Principle and two posts of Vice-Principal. Amongst the six candidates called for the interview, only two are eligible for the post of Principle 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
▶ Answer & Explanation
Correct answer: D. None of the above
To select one Principal from two eligible candidates, there are 2 choices. For the two Vice-Principal posts, all six candidates are eligible. The number of ways to choose 2 Vice-Principals from 6 is given by the combination formula C(n, k) = n! / (k! * (n-k)!), which is C(6, 2) = 6! / (2! * 4!) = (6*5) / (2*1) = 15. The total number of combinations is the product of the choices for each post: 2 * 15 = 30. Since 30 is not among the options A, B, or C, the correct answer is not listed.
Source: UPSC csat 2015