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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 ## How many different ways are there to arrange . . . tagged by: M7MBA ##### This topic has 1 expert reply and 1 member reply ### Top Member ## How many different ways are there to arrange . . . How many different ways are there to arrange a group of 3 adults and 4 children in 7 seats if adults must have the first, third, and 7 seats? A. 12 B. 144 C. 288 D. 1,400 E. 5,040 The OA is B. Can any expert give me a detailed explanation of how can I solve this PS question? Thanks. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Top Reply Hello M7MBA. We have to arrange 3 adults and 4 children in 7 seats in the following form: A C A C C C A. For the first place, we have 3 options. For the second place, we have 4 options. For the third place, we have 2 options. For the fourth place, we have 3 options. For the fifth place, we have 2 options. For the sixth place, we have 1 option. For the seventh place, we have 1 option. So, the total of options to arrange the 7 people is equal to 3*4*2*3*2*1*1 = 144. So, the correct answer is B. I hope this explanation may help you. Feel free to ask me again if you have a doubt. Regards. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. Master | Next Rank: 500 Posts Joined 29 Nov 2017 Posted: 100 messages Upvotes: 14 M7MBA wrote: How many different ways are there to arrange a group of 3 adults and 4 children in 7 seats if adults must have the first, third, and 7 seats? A. 12 B. 144 C. 288 D. 1,400 E. 5,040 The OA is B. Can any expert give me a detailed explanation of how can I solve this PS question? Thanks. three adults can be placed in three seats in 3! ways = 3*2*!=6 four children can be placed in four seats in 4! ways =4*3*2*1=24 Hence total number of ways = 6*24= 144 So B is the correct option. • Free Practice Test & Review How would you score if you took the GMAT 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 • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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