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A photographer is to take group photographs of a class of students for

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A photographer is to take group photographs of a class of students for [#permalink]

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New post 07 Oct 2016, 01:38
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A photographer is to take group photographs of a class of students for the school magazine such that each photograph should have five students. If there are four girls and four boys in the class and each photograph must not have two girls or two boys standing together, how many different photographs can the photographer take?

A. 80
B. 288
C. 4^4
D. 576
E. 288^2
[Reveal] Spoiler: OA

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Re: A photographer is to take group photographs of a class of students for [#permalink]

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New post 07 Oct 2016, 08:35
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Bunuel wrote:
A photographer is to take group photographs of a class of students for the school magazine such that each photograph should have five students. If there are four girls and four boys in the class and each photograph must not have two girls or two boys standing together, how many different photographs can the photographer take?

A. 80
B. 288
C. 4^4
D. 576
E. 288^2


Hi
The condition that TWO boys or TWO girls cannot be together means they should be alternate..
Total five means 3 of one and 2 of other..

1) choose 3 girls and arrange them... 4C3*3! = 4!= 24
2 boys can be choosen in 4C2 and arrange them in 2! Ways... 4C2*2!= 12
Total ways = 24*12 = 288..

2) same as above.. 2 girls and 3 boys.. 288

Total 288*2=576

D
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Re: A photographer is to take group photographs of a class of students for [#permalink]

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New post 07 Oct 2016, 12:25
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There are two different ways this can be arranged

GBGBG OR BGBGB

for option one we have 4*4*3*3*2=288 then multiply this by 2 for the second option=576
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Re: A photographer is to take group photographs of a class of students for [#permalink]

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New post 18 Oct 2017, 08:58
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Re: A photographer is to take group photographs of a class of students for   [#permalink] 18 Oct 2017, 08:58
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