In how many different ways can you seat 7 men and 3 women in

In how many different ways can you seat 7 men and 3 women in a row if the men all sit together and the women all sit together? How many ways are there for seven men and three women to stand in a line so that no two women stand next to each other?

Solution

(a) in this either man can go first or women can go first, so there are two possibilities so what ever be the combination will be multiplied by 2.

7 men can be arranged in 7! ways and women can be arranged in 3! ways.
so the answer is 2*7!*3!

(b) according to the condition no two women can sit together so lets start with men.

7 men can be arranged in 7! possible ways.
and three women can be arranged by 3C3 * 3! ways