GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 19 Jan 2020, 01:34

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

In how many ways can 5 apples (identical) be distributed among 4 ident

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

Hide Tags

Find Similar Topics 
Director
Director
User avatar
V
Joined: 24 Oct 2016
Posts: 586
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
In how many ways can 5 apples (identical) be distributed among 4 ident  [#permalink]

Show Tags

New post 22 May 2019, 16:01
1
6
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

29% (01:27) correct 71% (01:21) wrong based on 83 sessions

HideShow timer Statistics

In how many ways can 5 apples (identical) be distributed among 4 identical baskets?

A) 6
B) 20
C) 51
D) 56
E) 4^5
Director
Director
User avatar
V
Joined: 24 Oct 2016
Posts: 586
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
Re: In how many ways can 5 apples (identical) be distributed among 4 ident  [#permalink]

Show Tags

New post 22 May 2019, 16:02
2
dabaobao wrote:
In how many ways can 5 apples (identical) be distributed among 4 identical baskets?

A) 6
B) 20
C) 51
D) 56
E) 4^5



Official Solution


Credit: Veritas Prep


As we have seen previously, 5 fruits can be split into 4 groups in the following ways: {5, 0, 0, 0}, {4, 1, 0, 0}, {3, 2, 0, 0}, {3, 1, 1, 0}, {2, 2, 1, 0}, {2, 1, 1, 1}

Here, {5, 0, 0, 0} means that one basket has all 5 apples and the rest of the baskets are empty. Since the baskets are all identical, there is only 1 way of doing this.
{4, 1, 0, 0} means that one basket has 4 apples, another one has 1 apple and the rest of the baskets are empty. Since the fruits and the baskets are all identical, there is again only 1 way of doing this.

You have to select neither the fruits nor the baskets since they are all identical. You only have to decide how to distribute the apples in 4 groups. Therefore, each one of these cases will give us only one different way of distributing the fruits. Since there are 6 such cases, there are only 6 different ways of distributing the fruits.

ANSWER: A
VP
VP
avatar
P
Joined: 24 Nov 2016
Posts: 1069
Location: United States
CAT Tests
In how many ways can 5 apples (identical) be distributed among 4 ident  [#permalink]

Show Tags

New post Updated on: 11 Dec 2019, 10:49
dabaobao wrote:
In how many ways can 5 apples (identical) be distributed among 4 identical baskets?

A) 6
B) 20
C) 51
D) 56
E) 4^5


Total partitions = 6
5000
4100
3200
3110
2111
2210

Ans (A)

Originally posted by exc4libur on 11 Dec 2019, 09:30.
Last edited by exc4libur on 11 Dec 2019, 10:49, edited 1 time in total.
Senior Manager
Senior Manager
avatar
G
Joined: 16 Feb 2015
Posts: 252
Location: United States
Concentration: Finance, Operations
Schools: INSEAD, ISB
Re: In how many ways can 5 apples (identical) be distributed among 4 ident  [#permalink]

Show Tags

New post 11 Dec 2019, 10:36
1
exc4libur wrote:
dabaobao wrote:
In how many ways can 5 apples (identical) be distributed among 4 identical baskets?

A) 6
B) 20
C) 51
D) 56
E) 4^5


Total partitions = 6
5000
4100
3200
3110
2111
2110 It Should be 2210

Ans (A)


Dear exc4libur ,

I think u made one typo mistake in your answer. I have highlighted it.
Please correct.

Regards,
Rajat Chopra
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9053
Location: United States (CA)
Re: In how many ways can 5 apples (identical) be distributed among 4 ident  [#permalink]

Show Tags

New post 12 Dec 2019, 19:49
dabaobao wrote:
In how many ways can 5 apples (identical) be distributed among 4 identical baskets?

A) 6
B) 20
C) 51
D) 56
E) 4^5


The 5 identical apples can be distributed among 4 identical baskets in the following ways:

{5, 0, 0, 0}

{4, 1, 0, 0}

{3, 2, 0, 0}

{3, 1, 1, 0}

{2, 2, 1, 0}

and

{2, 1, 1, 1}

We see that there are 6 ways.

(Note: Since the apples are identical and the baskets are also identical, a rearrangement such as {0, 1, 0, 4} is considered the same as {4, 1, 0, 0}.)

Answer: A
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
181 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Director
Director
User avatar
V
Joined: 28 Jul 2016
Posts: 769
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)
Reviews Badge
Re: In how many ways can 5 apples (identical) be distributed among 4 ident  [#permalink]

Show Tags

New post 14 Dec 2019, 21:48
Is here a mathematical formula to solve this question?
GMAT Club Bot
Re: In how many ways can 5 apples (identical) be distributed among 4 ident   [#permalink] 14 Dec 2019, 21:48
Display posts from previous: Sort by

In how many ways can 5 apples (identical) be distributed among 4 ident

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





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