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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 ## A group of 10 people consists of 3 married couples and 4 si ##### This topic has 2 expert replies and 0 member replies ## A group of 10 people consists of 3 married couples and 4 si ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult A group of 10 people consists of 3 married couples and 4 single men. A committee of 4 is to be fo from the 10 people. How many different committees can be formed if the committee can consist of at most 1 married couple? (A) 105 (B) 207 (C) 210 (D) 540 (E) 5,040 ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15257 messages Followed by: 1861 members Upvotes: 13060 GMAT Score: 790 subh2273 wrote: A group of 10 people consists of 3 married couples and 4 single men. A committee of 4 is to be fo from the 10 people. How many different committees can be formed if the committee can consist of at most 1 married couple? (A) 105 (B) 207 (C) 210 (D) 540 (E) 5,040 Good committees = total committees - bad committees. Total committees: From 10 people, the number of ways to choose 4 = 10C4 = (10*9*8*7)/(4*3*2*1) = 210. Bad committees: Since a good committee includes at most 1 married couple, a bad committee is composed of 2 married couples. From 3 married couples, the number of ways to choose 2 to form a 4-member committee = 3C2 = (3*2)/(2*1) = 3. Thus: Good committees = 210-3 = 207. 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 25 Apr 2015 Posted: 2444 messages Followed by: 18 members Upvotes: 43 subh2273 wrote: A group of 10 people consists of 3 married couples and 4 single men. A committee of 4 is to be fo from the 10 people. How many different committees can be formed if the committee can consist of at most 1 married couple? (A) 105 (B) 207 (C) 210 (D) 540 (E) 5,040 If there are no restrictions on how to select the 4 people from a group of 10 people, then we have: 10C4 = 10!/[4!(10-4)!] = 10!/(4!6!) = (10 x 9 x 8 x 7)/4! = (10 x 9 x 8 x 7)/(4 x 3 x 2 x 1) = 5 x 3 x 2 x 7 = 210 ways to select them. All of these ways will consist of at most 1 married couple, except if the 4 people picked consist of 2 married couples. So, letâ€™s determine the number of ways 2 married couples can be picked as a committee of 4: If a committee of 4 consists of 2 married couples, then it could be: (couple 1, couple 2), (couple 1, couple 3), or (couple 2, couple 3). Thus, there are only 3C2 = 3 ways that 2 married couples can be picked for the committee of 4. Subtract this from 210 and we have 207 ways to select a committee of 4 that will consist of at most 1 married couple. Answer: B _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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