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mandy
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Hello Everyone

5 boys and 5 Girls are made to stand in line such that no 2 girls stand next to each other . In How many way can the line be formed

from 4 gmat software

Plz explains your works and reasoning

thanks :)



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chuliu
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5!*6*5!
Boys line in first: 5!
Choose 5 gaps from 6 gaps between the boys: 6C5=6
Girls fill in the gaps: 5!
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Macedon
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chuliu
5!*6*5!
Boys line in first: 5!
Choose 5 gaps from 6 gaps between the boys: 6C5=6
Girls fill in the gaps: 5!
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so what's the outcome???

6* 5! ????? thanks
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nadia0410
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ps arrangement 07 Sep 2005, 07:52
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I think the answer is 2* 5!*5! or 28,800

Each girl can choose one of 5 spots (5!). Each boy can choose one of the remaining 5 spots (5!). But then the girls can take either the odd places or the even places, so we have to multiply it by 2.
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It's not just odd-even though. Problem says no two girls can stand next to each other, but not that no two boys can. So we have 6 possible combinations:

GBGBGBGBGB
BGBGBGBGBG
GBBGBGBGBG
GBGBBGBGBG
GBGBGBBGBG
GBGBGBGBBG

Each of those has (5!*5!) permutations. So I agree with Chuliu, the answer would be 5!*5!*6 or 86,400.
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Antmavel
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ps arrangement 07 Sep 2005, 08:47
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I found 9000 but I think I am lost on this one :cry:
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popew626
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coffeeloverfreak
It's not just odd-even though. Problem says no two girls can stand next to each other, but not that no two boys can. So we have 6 possible combinations:

GBGBGBGBGB
BGBGBGBGBG
GBBGBGBGBG
GBGBBGBGBG
GBGBGBBGBG
GBGBGBGBBG

Each of those has (5!*5!) permutations. So I agree with Chuliu, the answer would be 5!*5!*6 or 86,400.
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I didn't even think of two boys next to each other. GOD I HATE THESE PROBLEMS!!!! :twisted:
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mandy
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OA IS 5!*5!*6
thanks for yours feedbacks


mandy
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richardj
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I hope they aren't this hard in the real GMAT !



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