SOLUTION: In how many ways can Ray, Steve, Ben, Ann, Cindy, and Dolly line up so that no two of the three boys are next to each other?

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Question 1064532: In how many ways can Ray, Steve, Ben, Ann, Cindy, and Dolly line up so that no two of the three boys are next to each other?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
There are 4 possible line-ups by gender, B=boy, G=girl:

BGBGBG
GBGBGB
BGGBGB
BGBGGB

For each of those 4 line-ups by gender,

The 3 girls can be arranged in 3! or 6 ways
The 3 boys can also be arranged in 3! or 6 ways.

That's (4)(3!)(3!) = (4)(6)(6) = 144 ways.

Edwin