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:

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Rich
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ans C
Figure attached

Lets consider the group of all boys as one entity and group of girls as other entity

Now we have two entities to arrange which is possible in 2! ways

The group of boys within itself can be rearranged in 3! ways and
The group of Girls within itself can be rearranged in 3! ways

Total arrangements = 2!*3!*3! = 2*6*6 = 72

Answer: Option C
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Condition: girls not separated..and boys are not separated

Count them as 1&1. Now we have 1boys n 1girl..

Arrangements =2!
And arrangements inside 3 girls & inside 3boys is=3! & 3!

Total=2!*3!*3! = 72 option C

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Hi Al,

There are a number of ways to do the "math in this question", but here's a way that you might find easy:

The fact that we have 6 chairs in a row means that we'll likely be doing a permutation. We're given the specific rule that the seating will have to be either GGGBBB or BBBGGG.

The first chair can have either a boy or a girl:

6 _ _ _ _ _

Whether it's a boy or a girl, the next two chairs must be the same gender:

6 2 1 _ _ _

Then the next 3 chairs must be the other gender:

6 2 1 3 2 1

Now multiply:

6x2x1x3x2x1 = 72 possibilities.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****