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In how many different ways 3 girls and 3 boys be seated at..

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by BTGmoderatorLU » Mon Dec 11, 2017 6:25 am
In how many different ways 3 grils and 3 boys be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, is two grils or two boys can never sit side by side?

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

The OA is C.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
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by regor60 » Mon Dec 11, 2017 9:50 am
LUANDATO wrote:In how many different ways 3 grils and 3 boys be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, is two grils or two boys can never sit side by side?

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

The OA is C.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
One side of the table must be GBG and the other side must be BGB to satisfy that no same GMAT sits next to each other. The problem stipulates that one side has chairs and one stools as a cue that it matters which side the GBG and BGB sit.

So you are starting with 2 choices.

Put a girl into one of the GBG slots, there are 3 choices of girls. Put the other girl in the other spot, 2 choices. Now only one choice remains for a girl in the BGB spot. A total of 6 choices.

The boy placements follow the same patter, so 6 choices for the boys.

Total choices 2 *6*6 =72, C
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by [email protected] » Mon Dec 11, 2017 9:06 pm
Hi LUANDATO,

We're told that 3 girls and 3 boys will be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, and that two girls or two boys can never sit side-by-side. We're asked for the number of possible arrangements of the 6 children. While there are several ways to approach this question, it's ultimately a Permutation question.

To start, I'll label the seats....
ABC
DEF

ANY of the 6 children can sit in Seat A. Once we place one.....
There are 3 possible options for Seat B (since the opposite GMAT has to sit here). Once we place one...
There are 2 possible options for Seat C (the same GMAT that sat in Seat A). Once we place one....
There are 2 possible options for Seat D (the same GMAT that sat in Seat B). Once we place one....
There are 1 possible options for Seat E (the same GMAT that sat in Seat A and C).
There are 1 possible options for Seat F (the same GMAT that sat in Seat B and D).

Total arrangements = (6)(3)(2)(2)(1)(1) = 72

Final Answer: C

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