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First of all, the boys can be in any of 5! orders, if we ignore girls. Now imagine placing the girls after they boys are already in place. There are six spots for girls: Before the first boy, between the first and second, etc. The fact that no two girls can be adjacent means that no two can go in the same spot. The number of ways to place the girls is therefore (64)⋅4!. This gives us a total of (64)⋅5!⋅4!=6!5!2!=43200.
2 5 2
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