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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

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.

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?
_________________

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
_________________

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?

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.

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)?

Re: Four boys picked up 30 mangoes .In how many ways can they [#permalink]

Show Tags

19 Nov 2014, 20:55

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]

Show Tags

10 Jan 2016, 14:49

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.
_________________

Four boys picked up 30 mangoes .In how many ways can they [#permalink]

Show Tags

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

gmatclubot

Four boys picked up 30 mangoes .In how many ways can they
[#permalink]
28 Aug 2016, 05:45

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...