You can
put this solution on YOUR website! in how many ways can 4 boys and 5 girls be shifted in are room so that they
alternate?
They have to go
GBGBGBGBG, where G=girl, B=boy
The 5 girls can be arranged in the 5 positions labeled "G" in 5!=120 ways.
For each of those 120 ways to place the 5 girls in those 5 positions, there are
the 4 boys can be arranged in those 4 positions labeled "B" in 4!=24 ways.
Answer: (5!)(4!) = (120)(24) = 2880 ways.
Edwin
