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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 ## In how many ways four men, two women and one child can sit a tagged by: fskilnik@GMATH ##### This topic has 2 expert replies and 1 member reply ### GMAT/MBA Expert ## In how many ways four men, two women and one child can sit a ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult In how many ways four men, two women and one child can sit at a circular 7-seats table if the child is the only person to be seated between the two women? (A) 24 (B) 36 (C) 48 (D) 96 (E) 240 Answer: __(C)_____ Difficulty Level: 650 - 700 Source: www.GMATH.net _________________ Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version) Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount! ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 14929 messages Followed by: 1855 members Upvotes: 13060 GMAT Score: 790 fskilnik wrote: In how many ways four men, two women and one child can sit at a circular 7-seats table if the child is the only person to be seated between the two women? (A) 24 (B) 36 (C) 48 (D) 96 (E) 240 Once the child has been placed at the table: Number of ways to arrange the 2 women in the 2 seats adjacent to the child = 2! = 2. Number of ways to arrange the 4 men in the remaining 4 seats = 4! = 24. To combine these options, we multiply: 2*24 = 48. The correct answer is C. _________________ 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 Last edited by GMATGuruNY on Mon Sep 24, 2018 3:08 pm; edited 1 time in total 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 09 Oct 2010 Posted: 971 messages Followed by: 27 members Upvotes: 59 fskilnik wrote: In how many ways four men, two women and one child can sit at a circular 7-seats table if the child is the only person to be seated between the two women? (A) 24 (B) 36 (C) 48 (D) 96 (E) 240 Source: www.GMATH.net Thank you for the nice contribution, Mitch! (I believe this is the most direct - hence the better - argument, by the way.) Alternate solution: LetÂ´s imagine a linear version (=row), but "connecting the first seat to the last one" (so that after the last seat we have again the first one). There are 7 seats in which the child could be seated. Once (any) one of the 7 seats is chosen, there are 2 ways to seat the two women. (If the child is in the 7th seat, W1 will be in the 6th, W2 in the 1st... or vice-versa!) Once the child and the two women are seated, there are 4! ways of seating the men. Using the Multiplicative Principle, we have 7*2*4! ways of seating these people in the linear version. The "linear to circular migration" is done dividing 7*2*4! by the number of objects to be circularized (7), checking the "connection" created earlier do not give rise to unwanted configurations: it does not! (*) Hence: $? = \frac{{7 \cdot 2 \cdot 4!}}{7} = 48$ (*) Typical problem: when A and B cannot stay next to each other, in the linear version you cannot allow one of them to be in the first place and the other in the last place, because when the connection is established they would violate the restriction! This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version) Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount! Last edited by fskilnik@GMATH on Thu Sep 27, 2018 3:36 pm; edited 2 times in total ### Top Member Legendary Member Joined 29 Oct 2017 Posted: 680 messages Followed by: 4 members Let women be numbered as w1 and w2 and child be as c The arrangement can be done as w1cw2 or w2cw1 I.e. 2 ways Now group the women children as one so in addition to 4 other men, there are 5 entities to be arranged in a circle which can be done in (n-1)! Ways = (5-1)!= 4!= 24 ways So total ways = 2*24 = 48 ways • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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