#### Question

It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?

#### Solution

5 men and 4 women are to be seated in a row such that the women occupy the even places.

The 5 men can be seated in 5! ways. For each arrangement, the 4 women can be seated only at the cross marked places (so that women occupy the even places).

M x M x M x M x M

Therefore, the women can be seated in 4! ways.

Thus, possible number of arrangements = 4! × 5! = 24 × 120 = 2880

Is there an error in this question or solution?

Solution It is Required to Seat 5 Men and 4 Women in a Row So that the Women Occupy the Even Places. How Many Such Arrangements Are Possible? Concept: Concept of Combinations.