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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 ## Combinatorics problem tagged by: Brent@GMATPrepNow ##### This topic has 1 expert reply and 2 member replies ## Combinatorics problem Can someone please solve the following: How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0? A) 16 B) 27 C) 31 D) 32 E) 64 OA is D Legendary Member Joined 14 Aug 2012 Posted: 1556 messages Followed by: 34 members Upvotes: 448 Target GMAT Score: 750 GMAT Score: 650 (6c6 + 6c5 + 6c4 + 6c3 + 6c2 + 6c1) - (5c5 + 5c4 + 5c3 + 5c2 + 5c1) = (1 + 6 + 3x5 + 5x4 + 3x5 + 6) - (1 + 5 + 5x2 + 5x2 + 5) = (7 + 15 + 20 + 15 + 6) - (6 + 10 + 10 + 5) = 63 - 31 = 32 _________________ R A H U L ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13046 messages Followed by: 1253 members Upvotes: 5254 GMAT Score: 770 topspin360 wrote: How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0? A) 16 B) 27 C) 31 D) 32 E) 64 Here's another approach... Take the task of building subsets and break it into stages. Stage 1: Determine whether or not to place "0" in the subset The question tells us that "0" cannot be in the subset. So, we can complete stage 1 in 1 way (that is, we DO NOT place "0" in the subset Stage 2: Determine whether or not to place "1" in the subset We can either HAVE "1" in the subset or NOT HAVE "1" in the subset So, we can complete stage 2 in 2 ways Stage 3: Determine whether or not to place "2" in the subset We can either HAVE "2" in the subset or NOT HAVE "2" in the subset So, we can complete this stage in 2 ways Stage 4: Determine whether or not to place "3" in the subset We can either HAVE "3" in the subset or NOT HAVE "3" in the subset So, we can complete this stage in 2 ways Stage 5: Determine whether or not to place "4" in the subset We can complete this stage in 2 ways Stage 6: Determine whether or not to place "5" in the subset We can complete this stage in 2 ways By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus build all possible subsets ) in (1)(2)(2)(2)(2)(2) ways (= 32 ways = D) Cheers, Brent Aside: For more information about the FCP, watch our free video: http://www.gmatprepnow.com/module/gmat-counting?id=775 _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources Last edited by Brent@GMATPrepNow on Sat Jan 11, 2014 4:49 pm; edited 1 time in total GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! Master | Next Rank: 500 Posts Joined 25 Jul 2011 Posted: 468 messages Followed by: 4 members Upvotes: 29 alt way (5c5 + 5c4 + 5c3 + 5c2 + 5c1) + 1 empty set 31+1=32 • 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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