May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day!
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 07 Aug 2010
Posts: 1

Four boys picked up 30 mangoes .In how many ways can they
[#permalink]
Show Tags
07 Aug 2010, 06:26
Question Stats:
56% (00:56) correct 44% (00:00) wrong based on 31 sessions
HideShow timer Statistics
Four boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?




Math Expert
Joined: 02 Sep 2009
Posts: 55230

Re: solve these GMAT question
[#permalink]
Show Tags
08 Aug 2010, 04:51
likithae wrote: Four boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
help me to solve ......... 1. If boys can get zero mangoes them the answer would be  \((30+41)C(41)=33C3\):Consider 30 Mangoes: ****************************** and 3 separators . Permutations of these 33 symbols out of which 30 *'s and 3 's are identical is \(\frac{33!}{3!30!}\), or written in another way \(C^3_{33}\). Each permutation will mean one particular distribution of 30 mangoes among 4 boys: ****************************** first boy gets all mangoes; ****************************** first, second and third boys get 1 mango each, and fourth gets 27; ***************************** first gets one mango, second boy gets zero, third boy get 1 and fourth gets 28; And so on. 2. If boys should get at least one mango then the answer would be  \((26+41)C(41)=29C3\) (basically we are distributing 26 mangoes):The same as above: we should jut give 1 mango to each boy and then distribute 26 mangoes left as in previous case. 26 Mangoes: ************************** and 3 separators . Permutations of these 29 symbols out of which 26 *'s and 3 's are identical is \(\frac{29!}{3!26!}\), or written in another way \(C^3_{29}\). Again each permutation will mean one particular distribution of 26 mangoes among 4 boys. Similar problems: voucher98225.html?hilit=separatorsintegerslessthan85291.html?hilit=identical#p710836Direct formula: The total number of ways of dividing n identical items among r persons, each one of whom, can receive 0,1,2 or more items is \(n+r1C_{r1}\).
The total number of ways of dividing n identical items among r persons, each one of whom receives at least one item is \(n1C_{r1}\).P.S. 4^30 would be the answer if all mangoes were different but we are told that they are identical. Hope it helps.
_________________




Intern
Joined: 15 Jul 2010
Posts: 1

Re: solve these GMAT question
[#permalink]
Show Tags
07 Aug 2010, 07:39
Each Mango can be given to any one of the four people or in other words..1 mango can be divided into 4 ways...so all 30 can be divided in 4^30 ways..hops this helps



Director
Status: Apply  Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 18 Jul 2010
Posts: 603
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas

Re: solve these GMAT question
[#permalink]
Show Tags
08 Aug 2010, 09:24
Great analysis. I keep getting confused on such problems as to how to divide it up between so many persons. As the previous post suggested 4^30 seemed to make sense but then they are identical, so that is not correct. Let me ask this: 4^30 is correct number of distributing 30 different mangoes between 4 persons, if each gets 0,1,2... What if each has to get at least 1, 2, 3.. what would be the answer in that case with different mangoes?
_________________
Consider kudos, they are good for health



Manager
Joined: 20 Dec 2010
Posts: 182
Schools: UNC Duke Kellogg

Re: solve these GMAT question
[#permalink]
Show Tags
02 Jul 2011, 18:31
Excellent explanation from Bunuel  "stars and bars" method unleashed!
Basically "indistinguishable" balls into "distinguishable" urns...
30 "indistinguishable" mangoes into 4 "distinguishable" boys..
33C30
ANS: 5456



Manager
Joined: 27 Feb 2012
Posts: 118

Re: solve these GMAT question
[#permalink]
Show Tags
25 May 2013, 23:38
mainhoon wrote: Great analysis. I keep getting confused on such problems as to how to divide it up between so many persons. As the previous post suggested 4^30 seemed to make sense but then they are identical, so that is not correct. Let me ask this:
4^30 is correct number of distributing 30 different mangoes between 4 persons, if each gets 0,1,2... What if each has to get at least 1, 2, 3.. what would be the answer in that case with different mangoes? Hey can you explain me the logic for identical and nonidentical stuff? I am good with explanation above but 4^30 is also making sense to me. What makes it different from 33 C 3
_________________

Please +1 KUDO if my post helps. Thank you.



Manager
Joined: 14 Nov 2011
Posts: 117
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE: Consulting (Manufacturing)

Re: solve these GMAT question
[#permalink]
Show Tags
26 May 2013, 03:37
mainhoon wrote: Great analysis. I keep getting confused on such problems as to how to divide it up between so many persons. As the previous post suggested 4^30 seemed to make sense but then they are identical, so that is not correct. Let me ask this:
4^30 is correct number of distributing 30 different mangoes between 4 persons, if each gets 0,1,2... What if each has to get at least 1, 2, 3.. what would be the answer in that case with different mangoes? Hi Bunnel,, Can you please answer the above query?



Manager
Joined: 12 Feb 2012
Posts: 121

Re: solve these GMAT question
[#permalink]
Show Tags
03 Sep 2013, 06:16
Bunuel wrote: likithae wrote: Four boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
help me to solve ......... 1. If boys can get zero mangoes them the answer would be  \((30+41)C(41)=33C3\):Consider 30 Mangoes: ****************************** and 3 separators . Permutations of these 33 symbols out of which 30 *'s and 3 's are identical is \(\frac{33!}{3!30!}\), or written in another way \(C^3_{33}\). Each permutation will mean one particular distribution of 30 mangoes among 4 boys: ****************************** first boy gets all mangoes; ****************************** first, second and third boys get 1 mango each, and fourth gets 27; ***************************** first gets one mango, second boy gets zero, third boy get 1 and fourth gets 28; And so on. 2. If boys should get at least one mango then the answer would be  \((26+41)C(41)=29C3\) (basically we are distributing 26 mangoes):The same as above: we should jut give 1 mango to each boy and then distribute 26 mangoes left as in previous case. 26 Mangoes: ************************** and 3 separators . Permutations of these 29 symbols out of which 26 *'s and 3 's are identical is \(\frac{29!}{3!26!}\), or written in another way \(C^3_{29}\). Again each permutation will mean one particular distribution of 26 mangoes among 4 boys. Similar problems: voucher98225.html?hilit=separatorsintegerslessthan85291.html?hilit=identical#p710836Direct formula: The total number of ways of dividing n identical items among r persons, each one of whom, can receive 0,1,2 or more items is \(n+r1C_{r1}\).
The total number of ways of dividing n identical items among r persons, each one of whom receives at least one item is \(n1C_{r1}\).P.S. 4^30 would be the answer if all mangoes were different but we are told that they are identical. Hope it helps. Bunuel, Why is the same formula \(n+r1C_{r1}\) used for number of ways of dividing n identical items among r persons whom can receive can receive 0,1,2 or more items . Are you saying the same formula is used even if each person can receive 2 or 3 or anyitem? Why isn't that being factored in to the formula? How many ways are there to distribute 10 mangoes among 4 kids if each kid must receive at least 1 mango? How many ways are there to distribute 10 mangoes among 4 kids if each kid must receive at least 2 mango? How many ways are there to distribute 10 mangoes among 4 kids if each kid must receive at least 3 mango? Are you saying this formula gives us the same answer for all these questions? (10+41)C(41)?



Current Student
Joined: 08 Jan 2015
Posts: 75

Four boys picked up 30 mangoes .In how many ways can they
[#permalink]
Show Tags
28 Aug 2016, 06:45
Quote: Bunuel,
Why is the same formula \(n+r1C_{r1}\) used for number of ways of dividing n identical items among r persons whom can receive can receive 0,1,2 or more items . Are you saying the same formula is used even if each person can receive 2 or 3 or anyitem? Why isn't that being factored in to the formula?
How many ways are there to distribute 10 mangoes among 4 kids if each kid must receive at least 1 mango?
How many ways are there to distribute 10 mangoes among 4 kids if each kid must receive at least 2 mango?
How many ways are there to distribute 10 mangoes among 4 kids if each kid must receive at least 3 mango?
Are you saying this formula gives us the same answer for all these questions? (10+41)C(41)? I guess you already don't need a reply, but nevertheless: 1) 10 mangoes to 4 kids: We have 10 mangoes and 3 separators, so together 14 elements, then the number combinations is : \(\frac{13!}{3!10!}\) 2) 10 mangoes to 4 kids, if each one has to get at least 1 mango: First we give 1 mango to each, this leaves 6 mangoes, so we need to distribute this 6 mangoes to them => 6 mangoes and 3 separators: \(\frac{9!}{6!3!}\) 3) 10 mangoes to 4 kids, if one has to get at least 2 mangoes: First we give 2 mango to each, this leaves 2 mangoes, so we need to distribute this 2 mangoes to them => 2 mangoes and 3 separators: \(\frac{5!}{2!3!}\) 4) In order for each one to have 3 mangoes, the total number of mangoes has to be 12, so this option is not feasible



Manager
Joined: 21 Mar 2017
Posts: 54

Re: Four boys picked up 30 mangoes .In how many ways can they
[#permalink]
Show Tags
28 Jul 2017, 09:17
Bunuel wrote: likithae wrote: Four boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?
help me to solve ......... 1. If boys can get zero mangoes them the answer would be  \((30+41)C(41)=33C3\):Consider 30 Mangoes: ****************************** and 3 separators . Permutations of these 33 symbols out of which 30 *'s and 3 's are identical is \(\frac{33!}{3!30!}\), or written in another way \(C^3_{33}\). Each permutation will mean one particular distribution of 30 mangoes among 4 boys: ****************************** first boy gets all mangoes; ****************************** first, second and third boys get 1 mango each, and fourth gets 27; ***************************** first gets one mango, second boy gets zero, third boy get 1 and fourth gets 28; And so on. 2. If boys should get at least one mango then the answer would be  \((26+41)C(41)=29C3\) (basically we are distributing 26 mangoes):The same as above: we should jut give 1 mango to each boy and then distribute 26 mangoes left as in previous case. 26 Mangoes: ************************** and 3 separators . Permutations of these 29 symbols out of which 26 *'s and 3 's are identical is \(\frac{29!}{3!26!}\), or written in another way \(C^3_{29}\). Again each permutation will mean one particular distribution of 26 mangoes among 4 boys. Similar problems: http://gmatclub.com/forum/voucher98225 ... separatorshttp://gmatclub.com/forum/integersless ... al#p710836Direct formula: The total number of ways of dividing n identical items among r persons, each one of whom, can receive 0,1,2 or more items is \(n+r1C_{r1}\).
The total number of ways of dividing n identical items among r persons, each one of whom receives at least one item is \(n1C_{r1}\).P.S. 4^30 would be the answer if all mangoes were different but we are told that they are identical. Hope it helps. But I didn't find these equation of Gmat Club Math book. Isn't it imp?????



NonHuman User
Joined: 09 Sep 2013
Posts: 10981

Re: Four boys picked up 30 mangoes .In how many ways can they
[#permalink]
Show Tags
20 Oct 2018, 13:31
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: Four boys picked up 30 mangoes .In how many ways can they
[#permalink]
20 Oct 2018, 13:31






