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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 ## Basketball Representatives tagged by: Brent@GMATPrepNow ##### This topic has 2 expert replies and 2 member replies ## Basketball Representatives Hi everybody, Given that there are 5 basketball players per team, how many ways can you select 2 basketball players from 3 teams if no more than one player can be selected from each team? (A) 15 (B) 30 (C) 60 (D) 75 (E) 90 Please, help me to decide this task. Senior | Next Rank: 100 Posts Joined 12 Nov 2012 Posted: 85 messages Followed by: 2 members Upvotes: 8 Let's say we have team A, B, and C. Select 1 member from team A and 1 member from team B. This can be done in 5C1 * 5C1 = 25 ways. Similarly, you can select 1 member from team A and 1 member from team C. And also you can select 1 member from team C and 1 member from team B. Total number of selection = 25 *3 =75 ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13033 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 EOV wrote: Hi everybody, Given that there are 5 basketball players per team, how many ways can you select 2 basketball players from 3 teams if no more than one player can be selected from each team? (A) 15 (B) 30 (C) 60 (D) 75 (E) 90 Take the task of selecting 2 players and break it into stages. Stage 1: Select the 2 teams from which you will select 1 player each. Since the order in which we select the 2 teams does not matter. We can use combinations. There are 3 teams, and we must select 2 of them. This can be accomplished in 3C2 ways (3 ways). Stage 2: From one of the selected teams, select a player There are 5 players on that team, so we can accomplish this stage in 5 ways. Stage 3: From the other selected team, select a player There are 5 players on that team, so we can accomplish this stage in 5 ways. By the Fundamental Counting Principle (FCP) we can complete all 3 stages (and thus select 2 players) in (3)(5)(5) ways (= 75 ways = D) Cheers, Brent Aside: For more information about the FCP, we have a free video on the subject: http://www.gmatprepnow.com/module/gmat-counting?id=775 We also have a free video on calculating combinations (like 3C2) in your head: http://www.gmatprepnow.com/module/gmat-counting?id=789 _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15380 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 EOV wrote: Hi everybody, Given that there are 5 basketball players per team, how many ways can you select 2 basketball players from 3 teams if no more than one player can be selected from each team? (A) 15 (B) 30 (C) 60 (D) 75 (E) 90 Please, help me to decide this task. Number of options for the first player selected = 15. (Any of the 15 players.) Number of options for the second player selected = 10. (Any of the 10 players not on the same team as the first player.) To combine these options, we multiply: 15*10. Since the ORDER of the selections doesn't matter -- selecting AB is the same as selecting BA -- the product above must be divided by the number of ways to ARRANGE the two players selected (2!): (15*10)/(2*1) = 75. The correct answer is D. _________________ 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. Senior | Next Rank: 100 Posts Joined 22 Jul 2012 Posted: 30 messages Upvotes: 5 Please tell me if this way is right. Total Number of Selections - Ways to select 2 players from one team =15C2 - 3 ( 5C2) =105 - 30 =75 ANS = 75 • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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