Thread: Ordering people in a line

How many ways are there for eight men and five women to stand in a line so that no two women stand next to each other?

Can someone explain the solution step by step?
Thank you. =D

Hello, feiyingx!

How many ways are there for eight men and five women to stand in a line
so that no two women stand next to each other?

This approach seems to be the easiest . . .


Place the eight men in a row. .There are: ways.


Leave a space between the men (and on the ends):

. . _ M _ M _ M _ M _ M _ M _ M _ M _


To place the five women, we have a choice of nine spaces.
. . There are: choices.


Therefore, there are: .

Thanks a bunch for the response. xD It was really helpful.