Question

How many ways are there for 8 men and 12 women to stand in a line so that no three women stand next to each other?

Answer 1

Answer:

The answer is 609638400609638400, but no matter what I try I cannot reach that number. I have tried doing 2(8!5!/3!)∗(8!/5!)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