Question

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

• A. $2\times 2!$
• B. $24$
• C. $2x15!$
• D. $2!\times 13!$

Answer 1

The correct option is A

$2\times 2!$

Explanation for the correct option:

Finding the ways of seating arrangement:

Total number of members $=15$

The position of secretary vice secretary and principal are mixed but there is no condition of clockwise and anti-clockwise

Hence the total number of sitting ways according to the given condition $=2!$

As the position of three persons is fixed, we can change the position of $12$ members only

So the total number of ways of the seating arrangement of $12$ members $=12!$

Thus, the total number of ways in which $15$ members can be seated along with a circular table$=2!\times 12!$

Hence, option (A) is correct.