SOLUTION: 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? thanks a lot . . .

SOLUTION: 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? thanks a lot . . .

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Question 435577: 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?
thanks a lot . . .
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
First line up the men. There are 8! ways of doing that. Now put the 5 women in any of the 9 spaces possible (in-between the men, in front, at the back). This can be done in 9P5 ways. Hence there are 8!*9P5 = 609,638,400 total number of ways.
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