Three married couples are to be randomly assigned to 6 seats

Three married couples are to be randomly assigned to 6 seats in the same row at a concert. What is the probabilty that each married couple sits together? PLEASE GIVE A STEP BY STEP SOLUTION!!! THANKS!!!

Solution

Let us assume that each pair is closed in a box. So we only have three boxes to be arranged that can be done in 3! ways.

But each box has a couple who can interchange their position. So, for each box, number of possible arrangements = 2!.

So, for three boxes it will be 2! x 2! x 2!.

So, total number of possible arrangements = 3! x 2! x 2! x 2! = 48

And the total possible arrangements in any way = 6! = 720

So required probability = 48/720 = 1/15