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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 02 Jul 2015, 11:56
3
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

64% (02:32) correct 36% (02:36) wrong based on 59 sessions

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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. 44
D. 576
E. \(288^2\)

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

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New post 02 Jul 2015, 20:05
reto 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. 44
D. 576
E. \(288^2\)


Each Photograph must have 5 and no two boys or two girls should stand together. To make it happen there are two cases possible

Case-1: 3 Boys and 2 Girls are taken

Selection of 3 boys and 2 girls can be done in 4C3 * 4C2

Arrangement will look like B G B G B and Such arrangement of 5 individual can be done in desired manner in 3!*2! ways = 12 ways

No. of arrangement = 4C3 * 4C2 *3!*2! = 4*6*12 = 288



Case-2: 2 Boys and 3 Girls are taken

Selection of 2 boys and 3 girls can be done in 4C2 * 4C3

Arrangement will look like G B G B G and Such arrangement of 5 individual can be done in desired manner in 3!*2! ways = 12 ways

No. of arrangement = 4C2 * 4C3 *3!*2! = 4*6*12 = 288


Total Ways of Taking Photograph of 5 in desired manner = 288 + 288 = 576 ways

Answer: Option 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 02 Jul 2018, 09:29
I get 576.

There are 4 girls and 4 boys and we need 5 kids for photos without the same gender standing together. Hence, if we pick a boy for spot 1 (doesn't matter which gender), then there are 8 possibilities for spot 1.
Because we must pick the different gender for spot 2, there are 4 possibilities for spot 2.
Since we picked the first gender already, there are 3 possibilities for spot 3 and spot 4, respectively.
Finally, we have 2 possibilities for spot 5.

Thus: 8 * 4 * 3 * 3 * 2 = 576.
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Re: A photographer is to take group photographs of a class of students for &nbs [#permalink] 02 Jul 2018, 09:29
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