Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44298

In how many ways can 5 apples (identical) be distributed among 4 child [#permalink]
Show Tags
29 Sep 2015, 08:18
2
This post received KUDOS
Expert's post
16
This post was BOOKMARKED
Question Stats:
66% (01:27) correct 34% (01:47) wrong based on 179 sessions
HideShow timer Statistics



Current Student
Status: Mr
Joined: 05 Jul 2015
Posts: 46
Location: India
Concentration: Entrepreneurship, General Management
GMAT 1: 720 Q48 V40 GMAT 2: 770 Q50 V46
WE: Business Development (Advertising and PR)

Re: In how many ways can 5 apples (identical) be distributed among 4 child [#permalink]
Show Tags
29 Sep 2015, 12:27
1
This post received KUDOS
The answer is A. Here is how I found the answer Suppose we have five letter A’s representing apples. Let us also use three *’s which will represent partitions (four) between the apples belonging to different children. We order the A’s and *’s as we like and interpret all A’s before the first * as being apples belonging to Kathy. Now if you, the different ways these As and *s can be arranged, you will notice that each arrangement corresponds to a specific distribution. There are 5 As and 3 *s. The number of ways you can arrange them is [8!/(3!5!)] Generalised form for n = number of identical objects, and r = number of children is n+r1Cr1.



Current Student
Joined: 16 Jun 2015
Posts: 34
Concentration: Strategy, Social Entrepreneurship
WE: Information Technology (Other)

Re: In how many ways can 5 apples (identical) be distributed among 4 child [#permalink]
Show Tags
30 Sep 2015, 05:22
2
This post received KUDOS
Let's just represent apple by the letter A and assume that in order to distribute these apples to different people, we just need to partition them in to 4 baskets.
In order to partition the apples in to 4 baskets, we would need three Partition bars , as shown below:
A  A  AA  A Child 1 Child 2 Child 3 Child 4
So basically we have 3 identical partition bars and 5 identical apples, how many ways can we arrange these?
8!/5!3! = 56



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11270
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: In how many ways can 5 apples (identical) be distributed among 4 child [#permalink]
Show Tags
30 Sep 2015, 11:05
Hi camlan1990, This question comes with a bit of a 'twist.' Since the apples are IDENTICAL, you have to be careful about duplicate 'options'... For example: Giving 1 apple to child A and 1 apple to child B is the SAME as.... Giving 1 apple to child B and 1 apple to child A Since those duplicate options are NOT supposed to be counted twice, the Combination Formula is necessary (the solutions by icefrog and ankuragarwal1301 showcase that math). GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Manager
Joined: 29 Jul 2015
Posts: 159

In how many ways can 5 apples (identical) be distributed among 4 child [#permalink]
Show Tags
30 Sep 2015, 11:40
3
This post received KUDOS
1
This post was BOOKMARKED
Bunuel wrote: In how many ways can 5 apples (identical) be distributed among 4 children? (Some children may get no apples.)
(A) 56 (B) 144 (C) 200 (D) 256 (E) 312 Number of ways of dividing 'n' identical objects into 'r' groups such that each group can contain any number of objects is given by \(n+r1_C_{r1}\) So, The number of ways of dividing 5 apples among 4 children is \(5+41_C_{41}\) = \(8_{C_3}\) = \(\frac{8!}{5!*3!}\) = \(56\) Answer: A



Intern
Joined: 29 Apr 2015
Posts: 23
GPA: 3.89

Re: In how many ways can 5 apples (identical) be distributed among 4 child [#permalink]
Show Tags
01 Oct 2015, 16:13
kunal555 wrote: Bunuel wrote: In how many ways can 5 apples (identical) be distributed among 4 children? (Some children may get no apples.)
(A) 56 (B) 144 (C) 200 (D) 256 (E) 312 Number of ways of dividing 'n' identical objects into 'r' groups such that each group can contain any number of objects is given by \(n+r1_C_{r1}\) So, The number of ways of dividing 5 apples among 4 children is \(5+41_C_{41}\) = \(8_{C_3}\) = \(\frac{8!}{5!*3!}\) = \(56\) Answer: ADoes this specifically include zero, as in zero apples in a basket? If so, what formula would you use in the event that everyone had to have at least 1 apple? Can you merely reduce "n" by 1, since n cant be zero? Suppose this there the case with 20 apples and 4 baskets.



Manager
Joined: 29 Jul 2015
Posts: 159

In how many ways can 5 apples (identical) be distributed among 4 child [#permalink]
Show Tags
02 Oct 2015, 04:00
1
This post received KUDOS
1
This post was BOOKMARKED
ar500 wrote: kunal555 wrote: Bunuel wrote: In how many ways can 5 apples (identical) be distributed among 4 children? (Some children may get no apples.)
(A) 56 (B) 144 (C) 200 (D) 256 (E) 312 Number of ways of dividing 'n' identical objects into 'r' groups such that each group can contain any number of objects is given by \(n+r1_C_{r1}\) So, The number of ways of dividing 5 apples among 4 children is \(5+41_C_{41}\) = \(8_{C_3}\) = \(\frac{8!}{5!*3!}\) = \(56\) Answer: ADoes this specifically include zero, as in zero apples in a basket? If so, what formula would you use in the event that everyone had to have at least 1 apple? Can you merely reduce "n" by 1, since n cant be zero? Suppose this there the case with 20 apples and 4 baskets. Yes, the above formula includes zero. The number of ways of distributing 'n' identical objects amongst 'r' groups such that each group gets at least 1 object is given by \({n1}_C_{r1}\) The number of ways of distributing 20 apples among 4 baskets such that each basket has at least 1 apple is \({201}_C_{41}\) = \({19}_C_{3}\)



Intern
Joined: 15 Dec 2014
Posts: 3
Location: United States
Concentration: General Management, Finance
GPA: 3.9

In how many ways can 5 apples (identical) be distributed among 4 child [#permalink]
Show Tags
02 Oct 2015, 04:27
2
This post was BOOKMARKED
Quote: In how many ways can 5 apples (identical) be distributed among 4 children? (Some children may get no apples.)
(A) 56 (B) 144 (C) 200 (D) 256 (E) 312 I know a simple way to solve this problem. Consider it as an equation : A + B + C + D = 5. Where letters represent children and 5 = Apples. Just apply the formula : n+r1Cr1 where r = children and N = 5 i.e Apples. we will get answer as 56. Remember : This formula is used because question mentions that some children may get 0 apple. If this was not mentioned, there is a different formula to solve the question.



SVP
Joined: 08 Jul 2010
Posts: 2017
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: In how many ways can 5 apples (identical) be distributed among 4 child [#permalink]
Show Tags
02 Oct 2015, 21:21
Bunuel wrote: In how many ways can 5 apples (identical) be distributed among 4 children? (Some children may get no apples.)
(A) 56 (B) 144 (C) 200 (D) 256 (E) 312 This questions can be solved by a property that's useful for calculating WHOLE NUMBER Solutions (All NonNegative Solution)
Whole Solution of a linear Equation a+b+c+d+e+.... = n
where we have r variables (a, b, c, d, e)
is (n+r1)C(r1) Here we have, a+b+c+d = 5 so Whole no. solution of the equation = (5+41)C(41) = 8C3 = 56 Answer: option A
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



NonHuman User
Joined: 09 Sep 2013
Posts: 6527

Re: In how many ways can 5 apples (identical) be distributed among 4 child [#permalink]
Show Tags
17 Apr 2017, 21:02
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: In how many ways can 5 apples (identical) be distributed among 4 child
[#permalink]
17 Apr 2017, 21:02






