How to solve the problem (combinatorics)?

Question

Mathematics

In how many ways can 5 women and 5 men line up for a photo in such a way that neither two women nor two men stand together?

I sit and still can not find a solution. Please tell me the solution ... I want to understand how all the same it is solved.

Answer 1

Obviously, they should stand M-F-M-F-M-F-M-F-M-F or F-M-F-M-F-M-F-M-F-M.
In each of the options, an independent permutation of 5 men and an independent permutation of 5 women are visible. In total it turns out (5! * 5!) * 2 = 28800