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In how many different ways can 3 girls and 3 boys be seated at a recta

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In how many different ways can 3 girls and 3 boys be seated at a recta [#permalink]

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New post 30 Mar 2015, 10:35
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In how many different ways can 3 girls and 3 boys be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, if two girls or two boys can never sit side by side?

A. 24
B. 36
C. 72
D. 84
E. 96
[Reveal] Spoiler: OA

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Re: In how many different ways can 3 girls and 3 boys be seated at a recta [#permalink]

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New post 30 Mar 2015, 11:59
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Hi Awli,

The prompt gives us the specific restriction that a boy can't sit next to another boy and a girl can't sit next to another girl. Since there are chairs on one side of the table and stools on the other side of the table, we have to account for 2 possible seating arrangements:

BGB
GBG

and

GBG
BGB

From here, we can use a simple permutation to get to the answer:

Moving from left-to-right....
For the first "spot", there are 3 different boys to choose from
For the second "spot", there are 3 different girls to choose from
For the third "spot", there then 2 different boys to choose from
For the fourth "spot", there are then 2 different girls to choose form
For the fifth and sixth "spots", we have the 1 boy and 1 girl that are left

(3)(3)(2)(2)(1)(1) = 36 possible seating arrangements for each of the two options.

(36)(2) = 72

Final Answer:
[Reveal] Spoiler:
C


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Re: In how many different ways can 3 girls and 3 boys be seated at a recta [#permalink]

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New post 30 Mar 2015, 23:21
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Awli wrote:
In how many different ways can 3 girls and 3 boys be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, if two girls or two boys can never sit side by side?

A. 24
B. 36
C. 72
D. 84
E. 96


Since 3 people will be on each side, and no two boys/two girls can sit together, on one side you will have Boy-Girl-Boy arrangement and on the other side you will have Girl-Boy-Girl arrangement.
From the 3 boys, choose 2 in 3C2 ways and a girl in 3C1 ways. Now you have split the boys and girls into BGB and GBG.
For BGB, pick a side (either chairs or stools) in 2 ways.
The girl takes the center seat and the 2 boys can be arranged around the girl in 2! ways.
On the other side, the boy sits in the center and the girls are arranged on his two sides in 2! ways.

Total arrangements = 3C2 * 3C1 * 2 * 2! * 2! = 72 ways.

Answer (C)
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Re: In how many different ways can 3 girls and 3 boys be seated at a recta [#permalink]

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New post 07 May 2016, 07:51
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Awli wrote:
In how many different ways can 3 girls and 3 boys be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, if two girls or two boys can never sit side by side?

A. 24
B. 36
C. 72
D. 84
E. 96


ans C
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Re: In how many different ways can 3 girls and 3 boys be seated at a recta [#permalink]

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Re: In how many different ways can 3 girls and 3 boys be seated at a recta   [#permalink] 16 Dec 2017, 03:04
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