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

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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