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it isnt tough but i still didnt get it

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it isnt tough but i still didnt get it

by sana.noor » Mon Jul 22, 2013 12:36 pm
In how many ways can 5 boys and 3 girls be seated on 8 chairs so that no two girls are together?
A 5760
B 14400
C 480
D 56
E 40320

OA is B
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by GMATGuruNY » Mon Jul 22, 2013 12:47 pm
sana.noor wrote:In how many ways can 5 boys and 3 girls be seated on 8 chairs so that no two girls are together?
A 5760
B 14400
C 480
D 56
E 40320

OA is B
Number of ways to arrange the 5 boys = 5! = 120.

Each girl must occupy a position TO THE LEFT or TO THE RIGHT of a boy:
__B__B__B__B__B__
Number of options for the first girl = 6. (Any of the 6 slots above.)
Number of options for the second girl = 5. (Any of the 5 remaining slots.)
Number of options for the third girl = 4. (Any of the 4 remaining slots.)

To combine all of these options, we multiply:
120 * 6 * 5 * 4 = 14,400.

The correct answer is B.
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by Brent@GMATPrepNow » Mon Jul 22, 2013 12:47 pm
sana.noor wrote:In how many ways can 5 boys and 3 girls be seated on 8 chairs so that no two girls are together?
A 5760
B 14400
C 480
D 56
E 40320

OA is B
Here's how I would set this up:

Take 11 chairs (yes 11), and first seat the 5 boys in chairs 2, 4, 6, 8, and 10
_B_B_B_B_B_

Since we are arranging 5 unique things (boys), this step can be accomplished 5! ways (i.e., 120 ways).

Note: This arrangement prevents the girls from sitting together.

Now seat each of the 3 girls in one of the 6 remaining seats.
The first girl can sit in any of the 6 seats.
The second girl can sit in any of the 5 remaining seats.
The third girl can sit in any of the 4 remaining seats.
So, we can seat the three girls is (6)(5)(4) ways (i.e., 120 ways)

At this point, throw away the 3 empty seats, and you have 8 children seated.

So, the total number of ways to seat all of the boys and girls is (120)(120) = [spoiler]14400 = B[/spoiler]

Cheers,
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by mgm » Wed Jul 24, 2013 3:43 pm
I would consider the following to be a valid combination _B_BBBB_ - no two girls are sitting together with 8 chairs. Just curious how did we arrive to a 11 chair model ?
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by mgm » Wed Jul 24, 2013 3:50 pm
I am sorry , I get it now basically empty chairs will be taken away ..thanks Brent and Mitch you two are awesome...
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