can anyone please help.............There are six boys and six girls at a party. In how many ways can they be seated in a row if they must sit alternating boys and girls?

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can anyone please help.............There are six boys and six girls at a party. In how many ways can they be seated in a row if they must sit alternating boys and girls?

Mathematics
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12*6*5*5*4*4*3*3*2*2*1*1
This is what I would believe to be the solution: Assume the first seat is occupied by a boy... there are 6 possible boys that can sit in that seat. The next seat is occupied by one of six possible girls. The third seat then can be occupied by one of 5 boys (one is sitting in seat #1). And so on. This would give you 6x6x5x5x4x4x3x3x2x2. However, you should double this since we assumed a boy sat in the first seat-- there is also the possibility that a girl sits in the first seat. Therefore, the answer is: 2x6x6x5x5x4x4x3x3x2x2
the first person to sit down could be any gender, therefore any of the 12 people so the first entry should be 12 in my opinion. followed by the pattern i showed above.

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Other answers:

That's accounted for by the 2x
i concur

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