Chapter 6 - Section 6.3 - Permutations and Combinations - Exercises - Page 414: 24

1,207,084,032,000 ways

First let us make all the women stand in a line. The ways in which this could be done = 10! Then we let men stand in places where there is always a woman between them. We have 11 places where men can go. So the arrangement is given by $C$(11,6), as we have 11 spots and 6 men. Men can interchange their position in 6! ways. So total arrangements are given by 10!×$C$(11,6)×6! = 1,207,084,032,000