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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 ## Four people are to be selected to receive a modeling tagged by: VJesus12 ##### This topic has 3 expert replies and 0 member replies ## Four people are to be selected to receive a modeling Four people are to be selected to receive a modeling contract from a group of 10 men, 5 women and 2 children. How many ways are possible in which 2 men, one woman and one child will receive a contract? A. 90 B. 180 C. 225 D. 450 E. 900 The OA is the option D. What is the best approach to solving this PS question? Is there a fast and easy way? I'd be thankful for your help experts. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 VJesus12 wrote: Four people are to be selected to receive a modeling contract from a group of 10 men, 5 women and 2 children. How many ways are possible in which 2 men, one woman and one child will receive a contract? A. 90 B. 180 C. 225 D. 450 E. 900 The OA is the option D. What is the best approach to solving this PS question? Is there a fast and easy way? I'd be thankful for your help experts. Hello Vjesus12. Let's take a look at your question. We have to select 2 men from 10 (10C2), one woman form 5 (5C2) and one child form 2 (2C1). Hence, the number of ways is $$10C\ 2=\frac{10!}{8!\cdot2!}=\frac{10\cdot9\cdot8!}{8!\cdot2}=\frac{90}{2}=45$$ $$5C\ 1=\frac{5!}{4!\cdot1!}=\frac{5\cdot4!}{4!}=5$$ $$2C\ 1=\frac{2!}{1!\cdot1!}=2$$ Hence, the final answer is 45*5*2=450. Therefore, the correct answer is the option D. I hope this answer may help you. I'm available if you'd like a follow-up. 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. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 497 members Upvotes: 2867 GMAT Score: 800 Hi VJesus12, We're told that 4 people are to be selected to receive a modeling contract from a group of 10 men, 5 women and 2 children. We're asked for the number of possible ways in which 2 men, one woman and one child will receive a contract. You can answer this question by using the Combination Formula three times (although you really just have to use it once). Since we're choosing 2 men, 1 woman and 1 child from each of their respective groups, we have three calculations to perform: Men = choose 2 from a group of 10 = 10!/2!8! = (10)(9)/(2)(1) = 45 sets of 2 men Women = choose 1 from a group of 5 = that's 5 options (you could also write this as 5!/1!4! = 5/1 = 5) Children = choose 1 from a group of 2 = that's 2 options (you could also write this as 2!/1!1! = 2/1 = 2) To get the total number of possibilities, we have to multiply those 3 outcomes: (45)(5)(2) = 450 Final Answer: D GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 VJesus12 wrote: Four people are to be selected to receive a modeling contract from a group of 10 men, 5 women and 2 children. How many ways are possible in which 2 men, one woman and one child will receive a contract? A. 90 B. 180 C. 225 D. 450 E. 900 We are given that 4 people are to be selected for a modeling contract. We must determine, from 10 men, 5 women, and 2 children, the number of ways that 2 men, 1 woman, and 1 child will receive a contract. The number of ways that 2 men will receive a contract is 10C2 = (10 x 9)/2! = 45. The number of ways that 1 woman will receive a contract is 5C1 = 5. The number of ways that 1 child will receive a contact is 2C1 = 2. Thus, the number of ways such that 2 men, 1 woman, and 1 child will receive a contract is: 45 x 5 x 2 = 450 Answer: D _________________ 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. 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