How many ways are there for 10 women and 6 men to stand in a line so that no two men stand next to each other?
- Hint* Position the women and then consider possible positions for the men
Placing the women first you have 10! ways to place them. and then you have
[ ] W [ ] W [ ] W [ ] W [ ] W [ ] W [ ] W [ ] W [ ] W [ ] W [ ]
and the [ ] are possible places where you can put a man so there are 11 choose 6 ways to put the men somewhere.
$ 10!*11!/(5!) $
