QUESTION

CSAT

Easy

Maths

Prelims 2015

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:

Select an option to attempt

Explanation

Step 1: Selecting the Principal There are 2 eligible candidates for the Principal position, and we need to select 1 candidate for this post. So, the number of ways to select the Principal is: Ways to select Principal = $C(2,1) = 2$

Step 2: Selecting the Vice-Principal After selecting the Principal, 5 candidates remain for the Vice-Principal posts. We need to select 2 out of these 5 remaining candidates. The number of ways to select 2 candidates for the Vice-Principal position is: Ways to select Vice-Principal = $C(5,2) = \frac{(5 \times 4)}{(2 \times 1)} = 10$

Step 3: Total Combinations The total number of possible combinations is the product of the ways to select the Principal and the ways to select the Vice-Principal: Total combinations = Ways to select Principal $\times$ Ways to select Vice-Principal = $2 \times 10 = 20$