Arrange $n$ men and $n$ women in a row, alternating women and men. A group contains n men and n women. How many ways are there to arrange these people in a row if the men and women alternate?
I got as far as:
There are $n$ [MW] blocks. So there are $n!$ ways to arrange these blocks.
There are $n$ [WM] blocks. So there are $n!$ ways to arrange these blocks.
Which makes the total ways to arrange the men and women in alternating blocks $2(n!)$
The correct answer is $2(n!)^2$
Where does the second power come from?

Your solution doesn't take into account that $[M_1,W_1]$ and $[M_1,W_2]$ are valid combinations.
