# How would you use permutations to find the arrangements possible

How would you use permutations to find the arrangements possible if a line has 4 girls and 4 boys alternating boy girl boy girl?
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Step 1
Line of 4 boys: $4×3×2×1=4!=24$ possibilities.
Line of 4 girls: also $4!=24$ possibilities.
Step 2
Combination of the two: $4!×4!={24}^{2}=576$ posibilities.
If it doesn't matter whether the first is a boy or a girl, we'll have to double that to $2×576=1152$