Question

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
Step by step explanation is needed.. ​

Answer 1

Answer:

the answer is 12

hope this helps you

Answer 2

The number of possible combinations of selectees is 12.

Step-by-step explanation:

A selection is to be made for one post of Principal and two posts of Vice-Principal.

Among the six candidates, only two are eligible for the post of Principal.

So, number of ways of selecting one candidate out of two candidates for the post of Principal = $2_{C_{1} }$ = $\frac{2\times 1!}{1!}$ = 2 ways.

All candidates are eligible for the post of Vice-Principal.

After selection of 1 candidate for the post of Principal, only five candidates are remaining for the post of Vice-Principal.

So, number of ways of selecting two candidates out of five candidates for the post of Vice-Principal = $5_{C_{2} } = \frac{5\times 4\times 3!}{2!\times 3!}$ = 10 ways.

The number of possible combinations of selectees is 2 + 10 = 12.

Hence, the number of possible combinations of selectees is 12.