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

Jun 22, 2016

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

Explanation:

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 $2 \times 576 = 1152$