Table of Contents

## Question

There are 20 persons sitting in a circle. In that, there are 18 men and 2 sisters. How many arrangements are possible, in which the two sisters are always separated by a man?

**a. 18!*2**

b. 17!

c. 17!*2

d. 12

## Solution

Consider 1 man between two sisters as one group..For Circular arrangement , we have (n-1)! ways There are 18 mens , means 18 Group (n-1)! = (18-1)! So they can be arranged in 17! ways as circular The one man in between the two sisters can be out of any 18 men So,17!*18 = 18! The two sisters can be arranged in 2 ways..so 18!*2