# Thread: A question which my friend gave me

1. ## A question which my friend gave me

6 men and 3 women stand in a Straight line
How many diff ways can they stand such that no two women stand next to each other?

2. The men can arrange themselves in $6!$ ways in a line. Then women can stand in the $5$ gaps between the men as well as at the $2$ extreme ends of the line, so they can arrange themselves in ${\rm^7P_3}=7\times6\times5$ ways. Hence the total number of ways of arranging the $9$ people is $7\times6\times5\times6!=151\,200.$

3. I was assuming the men were indistinguishable for some reason. Too much Halloween last night