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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 ## A woman has seven cookies - four chocolate chip and three tagged by: BTGmoderatorLU ##### This topic has 2 expert replies and 0 member replies ### Top Member ## A woman has seven cookies - four chocolate chip and three ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: Manhattan Prep A woman has seven cookies - four chocolate chip and three oatmeal. She gives one cookie to each of her six children: Nicole, Ronit, Kim, Deborah, Mark, and Terrance. If Deborah will only eat the kind of cookie that Kim eats, in how many different ways can the cookies be distributed? A. 5040 B. 50 C. 25 D. 15 E. 12 The OA is D. ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1975 messages Followed by: 30 members Upvotes: 470 BTGmoderatorLU wrote: Source: Manhattan Prep A woman has seven cookies - four chocolate chip and three oatmeal. She gives one cookie to each of her six children: Nicole, Ronit, Kim, Deborah, Mark, and Terrance. If Deborah will only eat the kind of cookie that Kim eats, in how many different ways can the cookies be distributed? A. 5040 B. 50 C. 25 D. 15 E. 12 The OA is D. Since there are 7 cookies and they are to be distributed among 6 friends, one cookie will be left. Let's assume that the leftover cookie is eaten by the woman herself. She can eat of any type: Chocolate or Oatmeal. Case 1: Say Deborah and Kim eat Chocolate cookies. Thus, we have 2 Chocolate and 3 Oatmeal cookies, (a total of 5 cookies) to be distributed among Nicole, Ronit, Mark, Terrance, and the woman (5 persons). The number of ways, this can be done = 5!/(2!*3!) = (5.4.3.2.1.)/[(1.2)(1.2.3)] = 10 ways Case 2: Say Deborah and Kim eat Oatmeal cookies. Thus, we have 4 Chocolate and 1 Oatmeal cookie, (a total of 5 cookies) to be distributed among Nicole, Ronit, Mark, Terrance, and the woman (5 persons). The number of ways, this can be done = 5!/4! = (5.4.3.2.1.)/(1.2.3.4) = 5 ways Total number of ways = 10 + 5 = 15. The correct answer: D Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: Manhattan Review Mehdipatnam | Hyderabad GMAT Prep | Bangalore GMAT Courses | Dilsukhnagar GRE Prep | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15348 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorLU wrote: Source: Manhattan Prep A woman has seven cookies - four chocolate chip and three oatmeal. She gives one cookie to each of her six children: Nicole, Ronit, Kim, Deborah, Mark, and Terrance. If Deborah will only eat the kind of cookie that Kim eats, in how many different ways can the cookies be distributed? A. 5040 B. 50 C. 25 D. 15 E. 12 Alternate approach: Case 1: Deborah and Kim each receive an oatmeal cookie In this case, 4 chocolate chip cookies and 1 oatmeal cookie remain. The remaining oatmeal cookie has 5 options: Nicole, Ronit, Mark, Terrance, or no one. Total ways = 5. Case 2: Deborah and Kim each receive a chocolate chip cookie In this case, 3 oatmeal cookies and 2 chocolate chip cookies are left, with the result that 2 or 3 of the remaining children each receive an oatmeal cookie. From : The number of ways to choose 2 to receive an oatmeal cookie = 4C2 = (4*3)/(2*1) = 6. The number of ways to choose 3 to receive an oatmeal cookie = 4C3 = (4*3*2)/(3*2*1) = 4. Total ways = 6+4 = 10. Case 1 + Case 2 = 5 + 10 = 15. The correct answer is D. Alternatively, we can simply LIST the number of ways the cookies can be distributed among Nicole, Ronit, Mark, or Terrance in each case. Case 1: Deborah and Kim each receive an oatmeal cookie In this case, 4 chocolate chip cookies and 1 oatmeal cookie remain for Nicole, Ronit, Mark, and Terrance. Options: CCCC OCCC COCC CCOC CCCO Total ways = 5. Case 2: Deborah and Kim each receive a chocolate chip cookie In this case, 3 oatmeal cookies and 2 chocolate chip cookies remain for Nicole, Ronit, Mark, and Terrance. Options: COOO OCOO OOCO OOOC OOCC OCOC OCCO COOC COCO CCOO Total ways = 10. Case 1 + Case 2 = 5 + 10 = 15. _________________ 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. 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