Firstly, we'll fix the postions where the
women will be. We have
forms to do that. So, we'll obtain a row like:

The n+1 spaces represented by the underline positions will receive the men of the row. Then,

Since there is no women sitting together, we must write that
. It guarantees that there is at least one man between two consecutive women. We'll do some substitutions:

The equation (i) can be rewritten as:

We obtained a linear problem of non-negative integer solutions in (ii). The number of solutions to this type of problem are known: ![\dfrac{[(n)+(m-n+1)]!}{(n)!(m-n+1)!}=\dfrac{(m+1)!}{n!(m-n+1)!}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5B%28n%29%2B%28m-n%2B1%29%5D%21%7D%7B%28n%29%21%28m-n%2B1%29%21%7D%3D%5Cdfrac%7B%28m%2B1%29%21%7D%7Bn%21%28m-n%2B1%29%21%7D)
[I can write the proof if you want]
Now, we just have to calculate the number of forms to permute the men that are dispposed in the row: 
Multiplying all results:
