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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 ## Ten telegenic contestants with a variety of personality diso ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Ten telegenic contestants with a variety of personality diso ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Ten telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of five members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible? A. 120 B. 126 C. 252 D. 1200 E. 1260 OA C Source: Princeton Review ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12653 messages Followed by: 1245 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorDC wrote: Ten telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of five members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible? A. 120 B. 126 C. 252 D. 1200 E. 1260 Let's take the task of creating the teams and break it into stages. Stage 1: Select two 5 contestants to be in tribe A Since the order in which we select the contestants does not matter, we can use combinations. We can select 5 contestants from 10 contestants in 10C5 ways 10C5 = (10)(9)(8)(7)(6)/(5)(4)(3)(2)(1) = 252 So, we can complete stage 1 in 252 ways Stage 2: Place the remaining 5 people in tribe B There's only 1 way to place all 5 remaining people in tribe B So we can complete this stage in 1 way. By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create 2 tribes of 5 contestants each) in (252)(1) ways (= 252 ways) Answer: C -------------------------- Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: http://www.gmatprepnow.com/module/gmat-counting/video/775 You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat-counting/video/776 Then you can try solving the following questions: EASY - http://www.beatthegmat.com/what-should-be-the-answer-t267256.html - http://www.beatthegmat.com/counting-problem-company-recruitment-t244302.html - http://www.beatthegmat.com/picking-a-5-digit-code-with-an-odd-middle-digit-t273110.html - http://www.beatthegmat.com/permutation-combination-simple-one-t257412.html - http://www.beatthegmat.com/simple-one-t270061.html MEDIUM - http://www.beatthegmat.com/combinatorics-solution-explanation-t273194.html - http://www.beatthegmat.com/arabian-horses-good-one-t150703.html - http://www.beatthegmat.com/sub-sets-probability-t273337.html - http://www.beatthegmat.com/combinatorics-problem-t273180.html - http://www.beatthegmat.com/digits-numbers-t270127.html - http://www.beatthegmat.com/doubt-on-separator-method-t271047.html - http://www.beatthegmat.com/combinatorics-problem-t267079.html DIFFICULT - http://www.beatthegmat.com/wonderful-p-c-ques-t271001.html - http://www.beatthegmat.com/permutation-and-combination-t273915.html - http://www.beatthegmat.com/permutation-t122873.html - http://www.beatthegmat.com/no-two-ladies-sit-together-t275661.html - http://www.beatthegmat.com/combinations-t123249.html 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 Elite Legendary Member Joined 23 Jun 2013 Posted: 10071 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, For Test Takers who know the Combination Formula, this question is a fairly straight-forward prompt. If you DON'T know the Combination Formula though, then here's what it is and how to use it. Any time a prompt asks for "groups" or "combinations" of things, then the order of the things DOES NOT MATTER. For example, if a 2-person team consists of A and B, then A,B is the same as B,A --> thus, order does NOT matter. Mathematically though, you're allowed to count this team TWICE - A,B and B,A are the same team, so it should only be counted ONCE. The Combination Formula removes all of the "duplicates", leaving you with the unique combinations for whatever situation you're working with. The Combination Formula itself is: N!/[K!(N-K)!] N = the total number of items/people K = the size of the subgroup Here, we have 10 people and we're asked to form 2 groups of 5. For the first group, N = 10 and K = 5.... 10!/[5!5!] = (10)(9)(8)(7)(6)/(5)(4)(3)(2)(1) = 256 unique groups of 5 people Once you have formed that group of 5, then the remaining 5 form the other group (so there's no more math to do) Final Answer: C GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2006 messages Followed by: 14 members Upvotes: 43 BTGmoderatorDC wrote: Ten telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of five members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible? A. 120 B. 126 C. 252 D. 1200 E. 1260 OA C Source: Princeton Review The number of ways to select the first tribe is 10C5: 10C5 = (10!)/(10 - 5)! x 5! = (10 x 9 x 8 x 7 x 6)/(5 x 4 x 3 x 2 x 1) = 3 x 2 x 7 x 6 = 252 The next tribe can be selected in 5C5 = 1 way. So there are 252 x 1 = 252 ways to select the two tribes. Answer: C _________________ Scott Woodbury-Stewart Founder and CEO • Award-winning private GMAT tutoring Register now and save up to$200

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