Question

Mother, Father and their six children $\left(3boysand3girls\right)$ are to be seated along a round table. How many ways can this be done if mother and father sit together and the males and females alternate?

Answer 1

In this problem there are $8$ family member.

Here mother can seat anywhere, Hence father has only $2!$ ways to seat either side of the mother

Now Boys has to seat alternate Hence they have only $3!$ ways to seat

And also Girls has to seat alternate Hence they have only $3!$ ways to seat

Total no of ways will be $3!3!2!=72$