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?

Answer 1

there are 20 persons in total and two sisters are seperated by a man.
Let M---> man S--> sister
let us consider SMS as one unit
so items left = 17+ 1(SMS)=18
so these 18 items can be arranged in circular table in (n-1)! ways ie. 17!*2!(two sisters can be arranged in 2! ways)....

Answer 2

Hey mate!


If we consider the two sister and the person in between the brothers as a block, then there will 17 others and this block of three people to be arranged around a circle.

The number of ways of arranging 18 objects around a circle is in 17! ways. 

Now the sister can be arranged on either side of the person who is in between the brothers in 2! ways.

The person who sits in between the two brothers could be any of the 18 in the group and can be selected in 18 ways.

Therefore, the total number of ways 18×17!×2= 2 × 18!..........................(18!= 18*17! )


#Be Brainly ✌✌