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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 committee of 6 is chosen from 8 men and 5 women so as to tagged by: swerve ##### This topic has 3 expert replies and 0 member replies ### Top Member ## A committee of 6 is chosen from 8 men and 5 women so as to ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult A committee of 6 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed? A. 635 B. 700 C. 1404 D. 2620 E. 3510 The OA is B Source: Economist GMAT ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12735 messages Followed by: 1246 members Upvotes: 5254 GMAT Score: 770 swerve wrote: A committee of 6 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed? A. 635 B. 700 C. 1404 D. 2620 E. 3510 Since the committee must have 6 people, there are two cases that meet the given restrictions: 1) The committee has 2 men and 4 women 2) The committee has 3 men and 3 women 1) The committee has 2 men and 4 women Since the order in which we select the men and women does not matter, we can use COMBINATIONS We can select 2 men from 8 men in 8C2 ways (= 28 ways) We can select 4 women from 5 women in 5C4 ways (= 5 ways) So, the total number of ways to select 2 men and 4 women = 28 x 5 = 140 2) The committee has 3 men and 3 women We can select 3 men from 8 men in 8C3 ways (= 56 ways) We can select 3 women from 5 women in 5C3 ways (= 10 ways) So, the total number of ways to select 2 men and 4 women = 56 x 10 = 560 So, the TOTAL number of ways to create the 6-person committee = 140 + 560 = 700 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 25 Apr 2015 Posted: 2215 messages Followed by: 17 members Upvotes: 43 swerve wrote: A committee of 6 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed? A. 635 B. 700 C. 1404 D. 2620 E. 3510 The OA is B Source: Economist GMAT Since the committee of 6 must contain at least 2 men and 3 women, we can have two scenarios: 1) 2 men and 4 women, or 2) 3 men and 3 women Scenario 1): 2 men and 4 women. 2 men: 8C2 = (8 x 7)/2! = 28 4 women: 5C4 = 5 The committee of 2 men and 4 women can be selected in 28 x 5 = 140 ways. Scenario 2): 3 men and 3 women. 3 men: 8C3 = (8 x 7 x 6)/3! = 56 3 women: 5C3 = (5 x 4 x 3)/3! = 10 The committee of 3 men and 3 women can be selected in 56 x 10 = 560 ways So the total number of ways to select a committee is 140 + 560 = 700. Answer: B _________________ Scott Woodbury-Stewart Founder and CEO ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2215 messages Followed by: 17 members Upvotes: 43 swerve wrote: A committee of 6 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed? A. 635 B. 700 C. 1404 D. 2620 E. 3510 The OA is B Source: Economist GMAT Since the committee of 6 must contain at least 2 men and 3 women, we can have two scenarios: 1) 2 men and 4 women, or 2) 3 men and 3 women Scenario 1): 2 men and 4 women. 2 men: 8C2 = (8 x 7)/2! = 28 4 women: 5C4 = 5 The committee of 2 men and 4 women can be selected in 28 x 5 = 140 ways. Scenario 2): 3 men and 3 women. 3 men: 8C3 = (8 x 7 x 6)/3! = 56 3 women: 5C3 = (5 x 4 x 3)/3! = 10 The committee of 3 men and 3 women can be selected in 56 x 10 = 560 ways So the total number of ways to select a committee is 140 + 560 = 700. Answer: B _________________ Scott Woodbury-Stewart Founder and CEO • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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