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azureus88

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4 boys and 4 girls sit around 2 concentic circles such that there are 4 in each circle. In how many ways can they be seated if boys and girls sit around different circles.

Can someone tell me whats wrong with this:

If boys in inner circle, 3! ways to seat boys, 3! ways to seat girls, but boys can also be on outer circle so 2x3!x3!

Answer is 288.
 

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4 boys and 4 girls sit around 2 concentic circles such that there are 4 in each circle. In how many ways can they be seated if boys and girls sit around different circles.

Can someone tell me whats wrong with this:

If boys in inner circle, 3! ways to seat boys, 3! ways to seat girls, but boys can also be on outer circle so 2x3!x3!

Answer is 288.
once one group sits down you no longer have the rotation effect. so it's 2x3!x4!
 

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