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Allison and Barbara are part of an 8-member dance troupe.

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Allison and Barbara are part of an 8-member dance troupe.

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Allison and Barbara are part of an 8-member dance troupe. For the upcoming spring recital, the troupe will be divided into two 4-person ensembles and each ensemble will perform a specialized dance. What fraction of all the possible ensembles that include Allison will also include Barbara?

A. 1/4
B. 3/7
C. 1/2
D. 3/4
E. 6/7

The OA is B.

Please, can anyone explain this PS question? I can't get the correct answer. I need help. Thanks.

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Hi swerve,

We're told that Allison and Barbara are part of an 8-member dance troupe and that the troupe will be divided into two 4-person ensembles (with each ensemble performing a specialized dance). We're asked for the fraction of all the possible ensembles that include Allison AND Barbara. This question is a 'Combination Formula' question with a 'twist.'

Since there are 8 members and we're forming groups of 4, there will be 8!/4!(8-4)! = (8)(7)(6)(5)/(4)(3)(2)(1) = 70 possible groups of 4 for the 1st group.

The 'twist' is that once you have your 1st group of 4, the other 4 people will also form a DIFFERENT group of 4. In simple terms, Allison could be in the 1st group OR the 2nd group, so we have to consider both options.

Allison will take 1 of the 4 spots in a group, and if Barbara takes one of the other spots, then there would be 2 spots left for the 6 remaining dancers. The number of ways in which that could occur is 6!/2!(4!) = (6)(5)/(2)(1) = 15 groups of 4 with Allison AND Barbara.

Thus, the probability that Allison and Barbara would be on the 1st group is 15/70 = 3/14. However, since there are TWO groups (the 1st group and the 2nd group), the overall probability of Allison and Barbara being on the SAME group (regardless of which one it is) is (2)(3/14) = 6/14 = 3/7.

Final Answer: B

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

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Contact Rich at Rich.C@empowergmat.com

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swerve wrote:
Allison and Barbara are part of an 8-member dance troupe. For the upcoming spring recital, the troupe will be divided into two 4-person ensembles and each ensemble will perform a specialized dance. What fraction of all the possible ensembles that include Allison will also include Barbara?

A. 1/4
B. 3/7
C. 1/2
D. 3/4
E. 6/7
There are 7 people besides Allison.
From this pool of 7 people, 3 must be selected to join Allison's 4-person ensemble.
Thus -- from the pool of 7 people -- the probability that Barbara is among the 3 people selected = 3/7.

The correct answer is B.

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swerve wrote:
Allison and Barbara are part of an 8-member dance troupe. For the upcoming spring recital, the troupe will be divided into two 4-person ensembles and each ensemble will perform a specialized dance. What fraction of all the possible ensembles that include Allison will also include Barbara?

A. 1/4
B. 3/7
C. 1/2
D. 3/4
E. 6/7

The OA is B.

Please, can anyone explain this PS question? I can't get the correct answer. I need help. Thanks.
Asking,"What fraction of all the possible ensembles that include Allison will also include Barbara?" is the same as asking, "What is the probability that Allison are Barbara are in the same troupe?

Step 1: Place Allison in one of the troupes.

Step 2: Choose the 3 remaining people to be in Allison's troupe.
Ask, "What is the probability that Barbara is one of the 3 chosen?"
There are 7 people who can fill the remaining 3 spots in Allison's troupe.
So, Barbara has a 3/7 chance of being in Allison's troupe.

Answer = B

Cheers,
Brent

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Brent Hanneson – Creator of GMATPrepNow.com
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swerve wrote:
Allison and Barbara are part of an 8-member dance troupe. For the upcoming spring recital, the troupe will be divided into two 4-person ensembles and each ensemble will perform a specialized dance. What fraction of all the possible ensembles that include Allison will also include Barbara?

A. 1/4
B. 3/7
C. 1/2
D. 3/4
E. 6/7
Let’s first determine the number of ensembles that include Allison. Suppose that Allison has been chosen for one of the ensembles. The three remaining people in the ensemble can be chosen in 7C3 = (7 x 6 x 5)/(3 x 2) = 35 different ways.

Now, let’s determine the number of ensembles that include both Allison and Barbara. Suppose that they are both chosen as members in one of the ensembles. The remaining two people can be chosen in 6C2 = (6 x 5)/(2 x 1) = 15 different ways.

Thus, 15/35 = 3/7 of all the possible ensembles that include Allison also include Barbara.

Answer: B

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Jeffrey Miller Head of GMAT Instruction

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