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Six students - 3 boys and 3 girls - are to sit side by side for a make

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Six students - 3 boys and 3 girls - are to sit side by side for a make [#permalink]

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New post 08 Dec 2014, 05:23
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Tough and Tricky questions: Combinations.



Six students - 3 boys and 3 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?

A) 12
B) 36
C) 72
D) 240
E) 720

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[Reveal] Spoiler: OA

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Re: Six students - 3 boys and 3 girls - are to sit side by side for a make [#permalink]

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New post 08 Dec 2014, 05:41
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in order not to have two boys or two girls next to one another, we must make an alternate sitting arrangement. (B-G-B-G-B-G) or (G-B-G-B-G-B).
Total ways = 2C1*3!*3!
=2*6*6
=72

Ans - C
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Re: Six students - 3 boys and 3 girls - are to sit side by side for a make [#permalink]

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New post 08 Dec 2014, 06:20
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Six students - 3 boys and 3 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?

A) 12
B) 36
C) 72
D) 240
E) 720


The boys (B) and girls(G) can either be arranged as BGBGBG or GBGBGB.
Within the arrangement BGBGBG or GBGBGB, the boys can be arranged 3! ways and girls can be arranged 3! ways.

Therefore total number of ways boys and girls can be arranged = 2*3!*3!= 72 ways

Answer: C
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Re: Six students - 3 boys and 3 girls - are to sit side by side for a make [#permalink]

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New post 08 Dec 2014, 21:22
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We can have 2 arrangements:
BGBGBG or GBGBGB

3!*3!*2 = 6*6*2 = 72 ways.

Ans. C) 72
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Re: Six students - 3 boys and 3 girls - are to sit side by side for a make [#permalink]

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New post 20 Jan 2018, 06:45
Bunuel wrote:

Tough and Tricky questions: Combinations.



Six students - 3 boys and 3 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?

A) 12
B) 36
C) 72
D) 240
E) 720


Since no two boys and no two girls can sit next to one another we can have the following arrangements:

B-G-B-G-B-G or G-B-G-B-G-B

We see that either arrangement can be selected in the following ways:

We have 3 options for the first boy, then 3 options for the first girl, then 2 options for a boy, 2 options for a girl, and then finally 1 option for each boy and girl.

This can be done in 3 x 3 x 2 x 2 x 1 x 1 = 36 ways.

Since the second arrangement can also be done in 36 ways, there are 36 + 36 = 72 possible ways of making the arrangement of no two boys and no two girls sitting next to one another.

Answer: C
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Re: Six students - 3 boys and 3 girls - are to sit side by side for a make   [#permalink] 20 Jan 2018, 06:45
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