Question 972600
in how many ways can 4 boys and 5 girls be shifted in are room so that they
alternate?
<pre>
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</pre>