In how many ways can 15 members of a council sit along a circular table, when the secretary is to sit on one side of the chairman and the deputy secretary on the other side?

CONCEPT:

Circular permutation:

The number of ways to arrange n distinct things in a circular arrangement is given by: (n - 1)!

The number of ways to arrange n distinct things but all of them looks alike in a circular arrangement like arrangement of beads in a necklace; the arrangement of flowers in a garland is given by:

CALCULATION:

Given: 15 members are sitting around a circular table such that the secretary and deputy secretary on either side of the chairman

Let us consider the secretary, chairman and deputy secretary as one group.

So, the total number of members now = 13

As we know, the number of ways to arrange n distinct things in a circular arrangement is given by: (n - 1)!.

So, these 13 members can sit in a circular table in 12! ways.

The group consisting of secretary, chairman and deputy secretary can be arranged in 2 ways such that the secretary and deputy secretary on either side of the chairman.

So, 2 × 12! ways are there in 15 members can sit in a circular table such that the secretary and deputy secretary on either side of the chairman.

Hence, option C is the correct answer.