# 7 boys and 5 girls sitting in a row, if no 2 girls are sitting together, find the permutations.

it's the question of math&stat, the way I think is 12! (no restrictions) - the permutations that 2 girls sitting together. But there are repeated cases, and i've puzzled and I realized that there're many experts here, so I hope my problem can be solved, thanks.

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Could you say a little about the context of this question? How do you know the first digit? –  Noah Snyder Dec 16 '12 at 14:20
it's the hint.. –  Wong Kim Dec 16 '12 at 14:22
Thank you. :) i understood. –  Wong Kim Dec 16 '12 at 14:36

Two girls that are siting together we can see as one girl they can sit in two ways.Two girls out of 5 we can choose in $\binom{5}{2}$ and all diferent positions are $$2\cdot\binom{5}{2}\frac{(7+4)!}{7!4!}=6600$$