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There are two ways to look at this problem; gender or person.

Gender (M=Male, F=Female); There is only one way and that is MFMFMFMFM.

By person, you have 9 places to fill. The first is 5 males could be placed there, the next 4 females could be placed there, the next 4 males can be placed there, the next 3 females can be placed there and so forth. So in this instance there are 5*4*4*3*3*2*2*1*1 = 2880 arrangements.

Another way is

just 5!*4!=2880.

Here 5! is for men and 4! for women.

ie. Men can be arranged in 5 ways and women can be arranged in 4 ways.

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Q: 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?
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