How many ways 15 members of a committee can sit around the round table

1.	How many ways 15 members of a committee can sit around the round table whereas secretary sit on one side and vice secretary on other side of Director ?
Answer» Total number of members = 15 Here, the position of secretary, vice secretary and director are fixed but there is no condition of clockwise and anti clockwise. Hence, total number of sitting ways according to condition = 2! Now, we can change the position of 12 members only. Hence, total number sitting ways of 12 members = 12! Hence, total number of ways 15 member sit according to given condition = 12! × 2!

How many ways 15 members of a committee can sit around the round table whereas secretary sit on one side and vice secretary on other side of Director ?

Answer»

Total number of members = 15

Here, the position of secretary, vice secretary and director are fixed but there is no condition of clockwise and anti clockwise.

Hence, total number of sitting ways according to condition = 2!

Now, we can change the position of 12 members only.

Hence, total number sitting ways of 12 members = 12!

Hence, total number of ways 15 member sit according to given condition = 12! × 2!