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

Explanation

Number of Men = 5. Number of Women = 4.
Nine places are to be filled. In these 9 places, only four are even. Therefore 4 even places can be filled with 4 women in `.^(4)P_(4)=4!` ways. Also remaining 5 places can be filled up with 5 men in `.^(5)P_(5)=5!` ways.
`therefore` required number of arrangements
`= 4! xx 5! =(4xx3xx2xx1)xx(5xx4xx3xx2xx1)=24xx120=2880`