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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 a cricket team consisting of 5 batsmen, 4 tagged by: AAPL ##### This topic has 3 expert replies and 0 member replies ### Top Member ## In how many ways a cricket team consisting of 5 batsmen, 4 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult e-GMAT In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, and 1 wicketkeeper and 1 all-rounder can be selected from the pool of 7 batsmen, 6 bowlers, 3 wicketkeepers and 3 allrounders? A. 567 B. 1420 C. 2256 D. 2835 E. 5670 OA D ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15387 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 AAPL wrote: e-GMAT In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, and 1 wicketkeeper and 1 all-rounder can be selected from the pool of 7 batsmen, 6 bowlers, 3 wicketkeepers and 3 allrounders? A. 567 B. 1420 C. 2256 D. 2835 E. 5670 From 7 batsmen, the number of ways to choose 5 = 7C5 = (7*6*5*4*3)/(5*4*3*2*1) = 21. From 6 bowlers, the number of ways to choose 4 = 6C4 = (6*5*4*3)/(4*3*2*1) = 15. From 3 wicketkeepers, the number of ways to choose 1 = 3. From 3 allrounders, the number of ways to choose 1 = 3. To combine these options, we multiply: 21*15*3*3 = integer with a units digit of 5. The correct answer is D. _________________ 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 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 08 Dec 2008 Posted: 13046 messages Followed by: 1252 members Upvotes: 5254 GMAT Score: 770 AAPL wrote: e-GMAT In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, and 1 wicketkeeper and 1 all-rounder can be selected from the pool of 7 batsmen, 6 bowlers, 3 wicketkeepers and 3 allrounders? A. 567 B. 1420 C. 2256 D. 2835 E. 5670 OA D Take the task of creating a cricket team and break it into stages. Stage 1: Select 5 batsmen Since the order in which we select the batsmen does not matter, we can use combinations. We can select 5 batsmen from 7 batsmen in 7C5 ways (21 ways) So, we can complete stage 1 in 21 ways Stage 2: Select 4 bowlers Since the order in which we select the bowlers does not matter, we can use combinations. We can select 4 bowlers from 6 bowlers in 6C2 ways (15 ways) So, we can complete stage 2 in 15 ways Stage 3: Select 1 wicketkeeper There are 3 wicketkeepers from which to choose, so we can complete this stage in 3 ways. Stage 4: Select 1 all-rounder There are 3 all-rounders from which to choose, so we can complete this stage in 3 ways. By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create a cricket team) in (21)(15)(3)(3) ways ( = 2835 ways) Answer: D -------------------------- Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: http://www.gmatprepnow.com/module/gmat-counting/video/775 You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat-counting/video/776 Then you can try solving the following questions: EASY - https://www.beatthegmat.com/what-should-be-the-answer-t267256.html - https://www.beatthegmat.com/counting-problem-company-recruitment-t244302.html - https://www.beatthegmat.com/picking-a-5-digit-code-with-an-odd-middle-digit-t273110.html - https://www.beatthegmat.com/permutation-combination-simple-one-t257412.html - https://www.beatthegmat.com/simple-one-t270061.html MEDIUM - https://www.beatthegmat.com/combinatorics-solution-explanation-t273194.html - https://www.beatthegmat.com/arabian-horses-good-one-t150703.html - https://www.beatthegmat.com/sub-sets-probability-t273337.html - https://www.beatthegmat.com/combinatorics-problem-t273180.html - https://www.beatthegmat.com/digits-numbers-t270127.html - https://www.beatthegmat.com/doubt-on-separator-method-t271047.html - https://www.beatthegmat.com/combinatorics-problem-t267079.html DIFFICULT - https://www.beatthegmat.com/wonderful-p-c-ques-t271001.html - https://www.beatthegmat.com/permutation-and-combination-t273915.html - https://www.beatthegmat.com/permutation-t122873.html - https://www.beatthegmat.com/no-two-ladies-sit-together-t275661.html - https://www.beatthegmat.com/combinations-t123249.html Cheers, Brent _________________ 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 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! ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 AAPL wrote: e-GMAT In how many ways a cricket team consisting of 5 batsmen, 4 bowlers, and 1 wicketkeeper and 1 all-rounder can be selected from the pool of 7 batsmen, 6 bowlers, 3 wicketkeepers and 3 allrounders? A. 567 B. 1420 C. 2256 D. 2835 E. 5670 OA D The 5 batsmen can be chosen in 7C5 ways. The 4 bowlers can be chosen in 6C4 ways. One wicketkeeper and one all-rounder each can be chosen in 3C1 ways. In total, the team can be chosen in 7C5 x 6C4 x 3C1 x 3C1 = 7!/(5!2!) x 6!/(4!2!) x 3 x 3 = [(7 x 6)/2] x [(6x5)/2] x 3 x 3 = 7 x 3 x 3 x 5 x 3 x 3 = 2835 ways. 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. Read our reviews • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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