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

It is currently 07 Dec 2019, 05:33

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 we put 4 different balls in 3 different boxes whe

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 10 Sep 2016
Posts: 15
In how many ways can we put 4 different balls in 3 different boxes whe  [#permalink]

Show Tags

New post Updated on: 28 Sep 2016, 23:14
2
27
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

57% (01:15) correct 43% (01:42) wrong based on 182 sessions

HideShow timer Statistics

In how many ways can we put 4 different balls in 3 different boxes when any box can contain any number of balls?

A. 80
B. 81
C. 64
D. 63
E. 82

Answer: B.

Can someone please tell me why 4x4x4=64 is not the right answer?
There are 4 ways to fill the 1st box, and 4 ways to the 2nd box and 4 ways to fill the 3rd box..since it says that any box can contain any number of balls..i assumed that repetition is allowed.

Kindly explain.

Thanks alot!!!

Originally posted by geetgmat on 28 Sep 2016, 10:40.
Last edited by Bunuel on 28 Sep 2016, 23:14, edited 1 time in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4125
Location: Canada
Re: In how many ways can we put 4 different balls in 3 different boxes whe  [#permalink]

Show Tags

New post 28 Sep 2016, 15:23
4
Top Contributor
1
geetgmat wrote:
In how many ways can we put 4 different balls in 3 different boxes when any box can contain any number of balls?

80
81
64
63
82

Answer: B.

Can someone please tell me why 4x4x4=64 is not the right answer?
There are 4 ways to fill the 1st box, and 4 ways to the 2nd box and 4 ways to fill the 3rd box..since it says that any box can contain any number of balls..i assumed that repetition is allowed.

Kindly explain.

Thanks alot!!!


"There are 4 ways to fill the 1st box"
This assumes that the box needs to be filled.
No requirement for any one box to contain ANY balls.

On the other hand, every ball needs to be placed somewhere.
So, we need to examine the number of ways to place each ball. See my solution above.

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
General Discussion
Retired Moderator
avatar
G
Joined: 26 Nov 2012
Posts: 554
Re: In how many ways can we put 4 different balls in 3 different boxes whe  [#permalink]

Show Tags

New post 28 Sep 2016, 11:21
geetgmat wrote:
In how many ways can we put 4 different balls in 3 different boxes when any box can contain any number of balls?

80
81
64
63
82

Answer: B.

Can someone please tell me why 4x4x4=64 is not the right answer?
There are 4 ways to fill the 1st box, and 4 ways to the 2nd box and 4 ways to fill the 3rd box..since it says that any box can contain any number of balls..i assumed that repetition is allowed.

Kindly explain.

Thanks alot!!!


NOTE : The number of permutations/arrangments of n things , taken r at ta time when each item may be repeated once, twice...up to r times in any arrangement is \(n^r\) ways.

The first box can be filled in n ways, the second box can be filled in n ways(even though the first box is filled with one item, the same item can be used for filling the second box also because repetition is allowed), the third box can also be filled in n ways...

The rth box can be filled in n ways..

Now all the r boxes together can be filled in (n*n*n*....r times ) ie. \(n^r\) ways.

So \(3^4\) ways..

Hope it clears..
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4125
Location: Canada
Re: In how many ways can we put 4 different balls in 3 different boxes whe  [#permalink]

Show Tags

New post 28 Sep 2016, 15:20
1
Top Contributor
3
geetgmat wrote:
In how many ways can we put 4 different balls in 3 different boxes when any box can contain any number of balls?

A. 80
B. 81
C. 64
D. 63
E. 82


Take the task of distributing the 4 different balls and break it into stages.

Stage 1: Select a box for the 1st ball to go into.
There are 3 available boxes, so we can complete stage 1 in 3 ways

Stage 2: Select a box for the 2nd ball to go into.
There are 3 available boxes, so we can complete stage 2 in 3 ways

Stage 3: Select a box for the 3rd ball to go into.
There are 3 available boxes, so we can complete stage 3 in 3 ways

Stage 4: Select a box for the 4th ball to go into.
There are 3 available boxes, so we can complete stage 4 in 3 ways

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus distribute all 4 balls) in (3)(3)(3)(3)(4) ways (= 81 ways)

Answer:

RELATED VIDEO

_________________
Test confidently with gmatprepnow.com
Image
Intern
Intern
User avatar
B
Joined: 03 Feb 2017
Posts: 25
Re: In how many ways can we put 4 different balls in 3 different boxes whe  [#permalink]

Show Tags

New post 12 Mar 2017, 09:24
Since there are 3 boxes, we have

3 possibilities for the first ball
3 possibilities for the second ball
3 possibilities for the third ball
3 possibilities for the fourth ball

So, total number of possibilities is 3*3*3*3 = 81
Director
Director
User avatar
V
Joined: 27 May 2012
Posts: 945
Re: In how many ways can we put 4 different balls in 3 different boxes whe  [#permalink]

Show Tags

New post 30 Dec 2018, 12:40
GMATPrepNow wrote:
geetgmat wrote:
In how many ways can we put 4 different balls in 3 different boxes when any box can contain any number of balls?

80
81
64
63
82

Answer: B.

Can someone please tell me why 4x4x4=64 is not the right answer?
There are 4 ways to fill the 1st box, and 4 ways to the 2nd box and 4 ways to fill the 3rd box..since it says that any box can contain any number of balls..i assumed that repetition is allowed.

Kindly explain.

Thanks alot!!!


"There are 4 ways to fill the 1st box"
This assumes that the box needs to be filled.
No requirement for any one box to contain ANY balls.

On the other hand, every ball needs to be placed somewhere.
So, we need to examine the number of ways to place each ball. See my solution above.

Cheers,
Brent


How could people not give Kudos for such valuable information! Members please appreciate valuable contribution such as this one by giving Kudos! Thanks GMATPrepNow.
_________________
- Stne
Senior Manager
Senior Manager
User avatar
G
Joined: 19 Nov 2017
Posts: 250
Location: India
Schools: ISB
GMAT 1: 670 Q49 V32
GPA: 4
Premium Member
Re: In how many ways can we put 4 different balls in 3 different boxes whe  [#permalink]

Show Tags

New post 03 Mar 2019, 03:31
1
Another way to think about it by considering the number of balls in each box.

Situation 1
Box 1: 4 balls | 0 balls | 0 balls
Box 2: 0 balls | 4 balls | 0 balls
Box 3: 0 balls | 0 balls | 4 balls


So situation 1 has 3 different possibilities. Similarly, situation 2, 3, and 4 have 3 different possibilities each.

Situation 2
Box 1: 3 balls
Box 2: 1 balls
Box 3: 0 balls


Situation 3
Box 1: 2 balls
Box 2: 2 balls
Box 3: 0 balls


Situation 4
Box 1: 2 balls
Box 2: 1 balls
Box 3: 1 balls


Thus the total number of ways in which 4 different balls can be put in 3 different boxes when any box can contain any number of balls is
3 x 3 x 3 x 3 = 81
_________________

Vaibhav



Sky is the limit. 800 is the limit.

~GMAC
Director
Director
avatar
P
Joined: 24 Nov 2016
Posts: 927
Location: United States
In how many ways can we put 4 different balls in 3 different boxes whe  [#permalink]

Show Tags

New post 26 Aug 2019, 13:50
geetgmat wrote:
In how many ways can we put 4 different balls in 3 different boxes when any box can contain any number of balls?

A. 80
B. 81
C. 64
D. 63
E. 82


given: 4 dif balls, 3 dif boxes, any number per box;

\(4•4•4=81\)

\({400}={3!/2!}•4c4=3\) ("/2!" because 00 are identical)
\({310}={3!}•4c3=6•4=24\)
\({220}={3!}•4c2/2!=6•3=18\) ("/2!" because 22 is double counting)
\({211}={3!}•4c2=6•6=36\)
\({total}=3+24+18+36=81\)

Answer (B)
GMAT Club Bot
In how many ways can we put 4 different balls in 3 different boxes whe   [#permalink] 26 Aug 2019, 13:50
Display posts from previous: Sort by

In how many ways can we put 4 different balls in 3 different boxes whe

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





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