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Question Description Solutions for In how many ways can 10 similar chocolates be distributed among 4 children of different ages such that each child gets, at least, one chocolate.a)13C3b)10C4c)9C3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free. Here you can find the meaning of In how many ways can 10 similar chocolates be distributed among 4 children of different ages such that each child gets, at least, one chocolate.a)13C3b)10C4c)9C3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of In how many ways can 10 similar chocolates be distributed among 4 children of different ages such that each child gets, at least, one chocolate.a)13C3b)10C4c)9C3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for In how many ways can 10 similar chocolates be distributed among 4 children of different ages such that each child gets, at least, one chocolate.a)13C3b)10C4c)9C3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of In how many ways can 10 similar chocolates be distributed among 4 children of different ages such that each child gets, at least, one chocolate.a)13C3b)10C4c)9C3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice In how many ways can 10 similar chocolates be distributed among 4 children of different ages such that each child gets, at least, one chocolate.a)13C3b)10C4c)9C3d)None of the aboveCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice CAT tests. Union Public Service Commission (UPSC) has released the NDA Result II 2022 (Name Wise List) for the exam that was held on 4th September 2022. Earlier, the roll number wise list was released by the board. A total number of 400 vacancies will be filled for the UPSC NDA II 2022 exam. The selection process for the exam includes a Written Exam and SSB Interview. Candidates who get successful selection under UPSC NDA II will get a salary range between Rs. 15,600 to Rs. 39,100.
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In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
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Question Stats: Hide Show timer StatisticsIn how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.A) 10B) 15C) 21D) 28E) 56 SOURCE: http://www.GMATinsight.com _________________
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
Awamy wrote: why the formula of identical objects doen'st work here ? So in this question, since 6 identical chocolates have to be distributed among 3 distinct people, but everyone should get at least one, we will apply the second formula = (6-1) C (3-1) = 5C2 = 10, which is our answer
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
GMATinsight wrote: In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.A) 10B) 15C) 21D) 28E) 56 SOURCE: http://www.GMATinsight.com Hi# of chocolates distributed to each child -\(x_1, x_2, x_3\), where \(x_i > 0\)We have non-empty set:\(x_1 + x_2 + x_3 = 6\)We need to convert it into \(x_i >=0\) substituting each \(x_i\) with \(y_i = x_i - 1\). \(x_i = y_i +1\):\(y_1 + y_2 + y_3 = 3\)\(_{3+3-1}C_3 = _5C_3 = \frac{5*4}{2} = 10\)Answer A
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
GMATinsight wrote: In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.A) 10B) 15C) 21D) 28E) 56 SOURCE: http://www.GMATinsight.com \\since a child must get at least 1 chocolate, lets distribute 1 chocolate to each child first, and thus we are left with 3 chocolates to redistribute now we are in businesssince chocolates are identical, the remaining 3 chocolates can be distributed among 3 children as follows 5!_____3! 2!= 10, the answer hope this helpsthankscheers, and do consider some kudos, guys
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink] why the formula of identical objects doen'st work here ?
Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink] chetan2u Bunuel could you please explain how to solve this without (n-1)Cr-1 ... i wanna learn the concept
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
GMATinsight wrote: In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.A) 10B) 15C) 21D) 28E) 56 SOURCE: http://www.GMATinsight.com formula to use here we can take case that child may get 0 chocolate n-1Cr-1 ; n=6 . r= 3 5c2; 10IMO A
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
GMATinsight wrote: In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.A) 10B) 15C) 21D) 28E) 56 SOURCE: http://www.GMATinsight.com given: 6 identical chocs, 3 different kids, at least 1 each;\(k_1+k_2+k_3=6…(k_1'+1)+(k_2+1)+(k_3+1)=6…k_1'+k_2+k_3=3\)\(C(n+r-1,r-1)=(3+3-1,3-1)=\frac{5!}{2!3!}=10\)Answer (A)
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
GMATinsight wrote: In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.A) 10B) 15C) 21D) 28E) 56 SOURCE: http://www.GMATinsight.com The detailed solution to the above problem using two methods is explained in the attached video
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink]
GMATinsight wrote: In how many ways can 6 chocolates be distributed among 3 children? A child may get any number of chocolates from 1 to 6 and all the chocolates are identical.A) 10B) 15C) 21D) 28E) 56 SOURCE: http://www.GMATinsight.com Let the children be A, B, and C. So A can get 1, B can get 1 and C can get 4 chocolates. Of course, this is different from A gets 4, B 1, and C 1, or, A gets 1, B 4, and C 1. In the calculations below, we will show how 3 positive integers can sum to 6 and the number of ways the 3 numbers can be rearranged among A, B, and C (for example, the first calculation below describes the distribution of the 6 chocolates mentioned above): 1 + 1 + 4 = 63!/2! = 3 ways1 + 2 + 3 = 6 3! = 6 ways2 + 2 + 2 = 63!/3! = 1 wayTherefore, there are a total of 3 + 6 + 1 = 10 ways that 6 chocolates can be distributed to 3 children._________________
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Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink] Hello from the GMAT Club BumpBot!Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________
Re: In how many ways can 6 chocolates be distributed among 3 children? A c [#permalink] 22 Jan 2022, 09:50 |
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