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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 ## There are 6 children at a family reunion, 3 boys and 3 girls tagged by: BTGmoderatorLU ##### This topic has 3 expert replies and 1 member reply ### Top Member ## There are 6 children at a family reunion, 3 boys and 3 girls There are 6 children at a family reunion, 3 boys, and 3 girls. They will be lined up single-file for a photo, alternating genders. How many arrangements of the children are possible for this photo? A. 54 B. 72 C. 18 D. 81 E. 36 The OA is B. I'm confused by this PS question. Experts, any suggestion? I always have troubles with the combination questions.. Thanks in advance. ### GMAT/MBA Expert Legendary Member Joined 20 Jul 2017 Posted: 503 messages Followed by: 10 members Upvotes: 86 GMAT Score: 770 We know that we *must* alternate boys and girls. This means we have two options for the order of boys and girls: B--G--B--G--B--G or G--B--G--B--G--B Within each of these two options, the boys can be arranged in any order and the girls can be arranged in any order. So we can think about this problem as: 2 order options * possible arrangements of 3 boys * possible arrangements of 3 girls There are 3 boys and 3 girls. This means that the total number of arrangements for each is 3! - 3*2*1 = 6. So our equation is 2 order options * 6 arrangements of 3 boys * 6 arrangements of 3 girls 2 * 6 * 6 = 72 So there are 72 total arrangements of children available for the photo. _________________ Erika John - Content Manager/Lead Instructor https://gmat.prepscholar.com/gmat/s/ Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/ Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 9939 messages Followed by: 492 members Upvotes: 2867 GMAT Score: 800 Hi LUANDATO, We're told that 3 boys and 3 girls will be lined up single-file for a photo, alternating genders. We're asked for the number of arrangements of the children that are possible for this photo. This question is a fairly standard Permutation question with one small 'twist.' Since the first child in line can be EITHER a boy or a girl, there are 6 options for that 1st spot. Once you put someone there though, the 2nd spot must be the OTHER gender, so... there are 3 spots for the 2nd spot. From there, the genders are boy-girl-boy-girl or girl-boy-girl-boy (depending who was in the 1st spot... there are 2 spots for the 3rd spot. there are 2 spots for the 4th spot. there are 1 spots for the 5th spot. there are 1 spots for the 6th spot. Total arrangements = (6)(3)(2)(2)(1)(1) = 72 Final Answer: B GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 09 Apr 2015 Posted: 1461 messages Followed by: 17 members Upvotes: 39 LUANDATO wrote: There are 6 children at a family reunion, 3 boys, and 3 girls. They will be lined up single-file for a photo, alternating genders. How many arrangements of the children are possible for this photo? A. 54 B. 72 C. 18 D. 81 E. 36 We can have the following arrangements: BGBGBG or GBGBGB Since the number of people in the arrangement is the same, the number of arrangements for each is the same. Letâ€™s tackle the first arrangement. For the first position, we have 3 possible boys to choose from. For the second position, we have 3 girls to choose from. For the third position, we have 2 boys, and for the fourth position we have 2 girls, and for the fifth, there is 1 boy, and for the sixth, there is 1 girl. Thus: 3 x 3 x 2 x 2 x 1 x 1 = 36 ways So the total number of ways is 36 + 36 = 72 ways. Answer: B _________________ Jeffrey Miller Head of GMAT Instruction ### Top Member Legendary Member Joined 02 Mar 2018 Posted: 718 messages Followed by: 1 members Firstly, let us arrange the boys in a way that there is a gap that will be filled by a girl in between each boy. There are 3 boys to arrange in 3 positions. Therefore the number of permutation possible= $$3P_2$$ = 6ways Next, we fill up the remaining 3 gaps with 3 girls . Number of possible permutation = $$3P_2$$ = 6ways We have permuted the possibilities in this way B-G-B-G-B-G But we can also have the arrangement in this way: G-B-G-B-G-B This means that for every arrangement obtained earlier, there are 2 possible permutations. Therefore the total number of arrangement possible = 2 * [6*6] =72 possible arrangements we can confidently say option B is correct • Free Practice Test & Review How would you score if you took the GMAT 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 • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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