Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 24 May 2017, 03:45

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Combinatorics: balls put into boxes

Author Message
TAGS:

Hide Tags

Intern
Joined: 09 Jan 2014
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 1

4 equal balls into 5 equal boxes so that 3 boxes are full [#permalink]

Show Tags

09 Jan 2014, 17:31
n how many ways can 4 (distinguishable) balls be put into 5 (distinguishable) boxes so that exactly 3 boxes are not empty?

Intern
Joined: 09 Jan 2014
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 1

13 equal balls into 5 equal boxes so that 3 boxes are full [#permalink]

Show Tags

09 Jan 2014, 17:36
In how many ways can 13 (indistinguishable) balls be put into 5 (indistinguishable) boxes so that exactly 3 boxes are not empty?

Please provide steps how to get to the answer and how to think correctly.
Intern
Joined: 09 Jan 2014
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 1

9 blue equal balls and 1 red ball put into 5 different boxes [#permalink]

Show Tags

09 Jan 2014, 17:39
In how many ways can 9 blue balls (all the same) and 1 red ball be put into 5 (distinguishable) boxes?

Please provide steps how to get to the answer and how to think correctly.
Intern
Joined: 09 Jan 2014
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 1

Combinatorics: balls put into boxes [#permalink]

Show Tags

09 Jan 2014, 17:40
In how many ways can 7 (distinguishable) balls be put into 12 boxes (2 boxes are equaly green (indistinguishable) and 10 are equaly yellow (indistinguishable)?

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7370
Location: Pune, India
Followers: 2285

Kudos [?]: 15093 [1] , given: 224

Re: 4 equal balls into 5 equal boxes so that 3 boxes are full [#permalink]

Show Tags

09 Jan 2014, 21:43
1
KUDOS
Expert's post
Meitene007 wrote:
In how many ways can 4 (distinguishable) balls be put into 5 (distinguishable) boxes so that exactly 3 boxes are not empty?

Please note that you must provide options in PS questions.

4 distinct balls
5 distinct boxes - 2 must be empty

First choose the 2 boxes which will be empty in 5C2 ways.
Now you have 4 distinct balls and 3 distinct boxes. Since no box should be empty, the only distribution which will work is 2, 1, 1 i.e. 2 balls in one box and 1 each in other two boxes.
Choose the box which will have 2 balls in 3C1 ways. Choose the two balls that will go together in the box in 4C2 ways.
The other two balls will be distributed to the other two boxes in 2! ways.

Total ways = 5C2 * 3C1 * 4C2 * 2! = 360 ways
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Re: 4 equal balls into 5 equal boxes so that 3 boxes are full   [#permalink] 09 Jan 2014, 21:43
Similar topics Replies Last post
Similar
Topics:
4 Combinatorics 1 17 Jul 2015, 05:37
1 PS Combinatorics 5 25 Apr 2013, 06:22
7 Combinatorics Summary 7 18 Aug 2014, 01:04
Probability and Combinatorics 3 28 Apr 2010, 11:11
212 Math: Combinatorics 39 16 May 2017, 14:17
Display posts from previous: Sort by