I have a homework problem in my textbook that has stumped me so far. There is a similar one to it that has not been assigned and has an answer in the back of the textbook. It reads:
How many ways are there for 8 men and 5 women to stand in a line so that no two women stand next to each other?
The answer is 609638400, but no matter what I try I cannot reach that number. I have tried doing 2(8!5!/3!)*(8!/5!) since each woman must be paired with a man in order to prevent two women getting near each other, but of course it's the wrong answer. What am I doing wrong here?