# SOLUTION: In how many ways can five boys and six girls be seated in a row of eleven seats so that boys and girls occupy alternating seats?

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 Question 136959: In how many ways can five boys and six girls be seated in a row of eleven seats so that boys and girls occupy alternating seats? Answer by stanbon(57307)   (Show Source): You can put this solution on YOUR website!In how many ways can five boys and six girls be seated in a row of eleven seats so that boys and girls occupy alternating seats? ----------------- There are only 5 alternating seats for the girls. There are 5! ways to place the five girls in them: = 120 ways There will then by 6 seats left to seat the boys. The 6 boys can be placed in 6! ways in the six seats: = 720 ways ----------- Total # of ways: 120*720 = 86,400 ways ================ Cheers, Stan H.