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?

Answer 1

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).
\(M\times M\times M\times M\times M\)

Therefore, the women can be seated in 4! ways. 
Thus, possible number of arrangements = 4! × 5! = 24 × 120 = 2880