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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 ## Employees at a company will vote for an executive team of ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Employees at a company will vote for an executive team of ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Employees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams could be selected from the eight candidates? A. 56 B. 120 C. 210 D. 1120 E. 6720 OA D Source: Magoosh ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2012 messages Followed by: 14 members Upvotes: 43 Top Reply BTGmoderatorDC wrote: Employees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams could be selected from the eight candidates? A. 56 B. 120 C. 210 D. 1120 E. 6720 If each of the 5-member executive team has a different position, then there can be 8P5 ways to choose the 5 people from a total of 8 people. However, since 3 of 5-member team have the same position (warrant officer) and it doesn’t matter how we arrange them, we have to divide 8P5 by 3!. So the answer is: 8P5/3! = (8 x 7 x 6 x 5 x 4)/(3 x 2) = 8 x 7 x 5 x 4 = 1120 Alternate Solution: There are 8 candidates for president, and after the president is chosen, there are 7 remaining candidates for the position of treasurer. After these positions are filled, the remaining 3 positions can be filled by any of the 6 remaining members, therefore there are 6C3 = 6!/(3!*3!) = 20 ways of such a choice. In total, there are 8 x 7 x 20 = 1120 ways of forming the executive team. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1282 messages Followed by: 29 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: Employees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams could be selected from the eight candidates? A. 56 B. 120 C. 210 D. 1120 E. 6720 Source: Magoosh $? = \underbrace {C\left( {8,1} \right)}_{{\text{president}}} \cdot \underbrace {C\left( {7,1} \right)}_{{\text{treasurer}}} \cdot \underbrace {C\left( {6,3} \right)}_{{\text{3}}\,\,{\text{officers}}} = 8 \cdot 7 \cdot \frac{{6 \cdot 5 \cdot 4}}{{3 \cdot 2}} = 56 \cdot 20 = 1220$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15103 messages Followed by: 1859 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorDC wrote: Employees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams could be selected from the eight candidates? A. 56 B. 120 C. 210 D. 1120 E. 6720 Number of options for president = 8. (Any of the 8 candidates.) Number of options for treasurer = 7. (Any of the 7 remaining candidates.) From the 6 remaining people, the number of ways to choose 3 to serve as warrant officers = 6C3 = (6*5*4)/(3*2*1) = 20. To combine these options, we multiply: 8*7*20 = 1120. 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. • 1 Hour Free BEAT THE GMAT EXCLUSIVE 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 • FREE GMAT Exam Know how you'd score today for$0

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