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: .