How would you use permutations to find the arrangements possible if a line has 4 girls and 4 boys alternating boy girl boy girl?

1 Answer
Jun 22, 2016

In fact we are making two lines -- boys and girls, and then intertwine them.


Line of 4 boys: #4xx3xx2xx1=4! =24# possibilities.
Line of 4 girls: also #4! =24# possibilities.

Combination of the two: #4!xx4! =24^2=576# posibilities.

If it doesn't matter whether the first is a boy or a girl, we'll have to double that to #2xx576=1152#