GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Nov 2018, 01:47

INSEAD R1 Results This Week!

First Decision Reported on Decision Tracker  |  Join INSEAD Chat to Calm Your Nerves & Catch the Latest Action


Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

Four boys picked up 30 mangoes .In how many ways can they

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 06 Aug 2010
Posts: 1
Four boys picked up 30 mangoes .In how many ways can they  [#permalink]

Show Tags

New post 07 Aug 2010, 05:26
7
00:00
A
B
C
D
E

Difficulty:

(N/A)

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?
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50658
Re: solve these GMAT question  [#permalink]

Show Tags

New post 08 Aug 2010, 03:51
10
9
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 - \((30+4-1)C(4-1)=33C3\):

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 - \((26+4-1)C(4-1)=29C3\) (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:
voucher-98225.html?hilit=separators
integers-less-than-85291.html?hilit=identical#p710836

Direct 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 \(n+r-1C_{r-1}\).

The total number of ways of dividing n identical items among r persons, each one of whom receives at least one item is \(n-1C_{r-1}\).


P.S. 4^30 would be the answer if all mangoes were different but we are told that they are identical.

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Intern
Intern
avatar
Joined: 15 Jul 2010
Posts: 1
Re: solve these GMAT question  [#permalink]

Show Tags

New post 07 Aug 2010, 06:39
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
Director
avatar
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 17 Jul 2010
Posts: 628
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Re: solve these GMAT question  [#permalink]

Show Tags

New post 08 Aug 2010, 08:24
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
Manager
avatar
Joined: 20 Dec 2010
Posts: 197
Schools: UNC Duke Kellogg
Re: solve these GMAT question  [#permalink]

Show Tags

New post 02 Jul 2011, 17:31
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
Manager
avatar
Joined: 27 Feb 2012
Posts: 120
Re: solve these GMAT question  [#permalink]

Show Tags

New post 25 May 2013, 22:38
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
Manager
avatar
Joined: 14 Nov 2011
Posts: 126
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE: Consulting (Manufacturing)
GMAT ToolKit User
Re: solve these GMAT question  [#permalink]

Show Tags

New post 26 May 2013, 02:37
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
Manager
avatar
Joined: 12 Feb 2012
Posts: 125
Re: solve these GMAT question  [#permalink]

Show Tags

New post 03 Sep 2013, 05:16
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 - \((30+4-1)C(4-1)=33C3\):

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 - \((26+4-1)C(4-1)=29C3\) (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:
voucher-98225.html?hilit=separators
integers-less-than-85291.html?hilit=identical#p710836

Direct 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 \(n+r-1C_{r-1}\).

The total number of ways of dividing n identical items among r persons, each one of whom receives at least one item is \(n-1C_{r-1}\).


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 \(n+r-1C_{r-1}\) 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+4-1)C(4-1)?
Current Student
avatar
B
Joined: 08 Jan 2015
Posts: 80
GMAT ToolKit User
Four boys picked up 30 mangoes .In how many ways can they  [#permalink]

Show Tags

New post 28 Aug 2016, 05:45
Quote:
Bunuel,

Why is the same formula \(n+r-1C_{r-1}\) 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+4-1)C(4-1)?


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
Manager
avatar
B
Joined: 21 Mar 2017
Posts: 54
Re: Four boys picked up 30 mangoes .In how many ways can they  [#permalink]

Show Tags

New post 28 Jul 2017, 08:17
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 - \((30+4-1)C(4-1)=33C3\):

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 - \((26+4-1)C(4-1)=29C3\) (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/voucher-98225 ... separators
http://gmatclub.com/forum/integers-less ... al#p710836

Direct 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 \(n+r-1C_{r-1}\).

The total number of ways of dividing n identical items among r persons, each one of whom receives at least one item is \(n-1C_{r-1}\).


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?????
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8821
Premium Member
Re: Four boys picked up 30 mangoes .In how many ways can they  [#permalink]

Show Tags

New post 20 Oct 2018, 12:31
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: Four boys picked up 30 mangoes .In how many ways can they &nbs [#permalink] 20 Oct 2018, 12:31
Display posts from previous: Sort by

Four boys picked up 30 mangoes .In how many ways can they

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.