First we find the numerator of the probability.

The number of ways we can have this arrangement

M W M W M W M W M W

For each of the 5! ways to place the men there are 5! ways to place the
women. That's 5!*5! or (5!)²

But we could also have this arrangement:

W M W M W M W M W M

which is another (5!)²

So the numerator, which is the number of ways to have men and women in
alternate seats, is 2(5!)²

The denominator is the number of ways anybody can sit anywhere, which
is 10!

So the probability is


                           


Edwin