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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Allison and Barbara are part of an 8-member dance troupe. tagged by: swerve ##### This topic has 4 expert replies and 0 member replies ### Top Member ## Allison and Barbara are part of an 8-member dance troupe. ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult 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. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10112 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 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 _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15203 messages Followed by: 1861 members Upvotes: 13060 GMAT Score: 790 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. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12744 messages Followed by: 1247 members Upvotes: 5254 GMAT Score: 770 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 _________________ Brent Hanneson – Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 09 Apr 2015 Posted: 1461 messages Followed by: 18 members Upvotes: 39 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 _________________ Jeffrey Miller Head of GMAT Instruction • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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