Find all School-related info fast with the new School-Specific MBA Forum

It is currently 21 Oct 2014, 07:41

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Larry, Michael, and Doug have five donuts to share. If any

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Director
Director
User avatar
Joined: 07 Jun 2004
Posts: 618
Location: PA
Followers: 3

Kudos [?]: 191 [1] , given: 22

Larry, Michael, and Doug have five donuts to share. If any [#permalink] New post 04 Feb 2011, 15:05
1
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

50% (02:15) correct 50% (01:28) wrong based on 194 sessions
Larry, Michael, and Doug have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?

(A) 21
(B) 42
(C) 120
(D) 504
(E) 5040
[Reveal] Spoiler: OA

_________________

If the Q jogged your mind do Kudos me : )

Expert Post
8 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23351
Followers: 3604

Kudos [?]: 28710 [8] , given: 2815

Re: Combinations tough [#permalink] New post 04 Feb 2011, 15:20
8
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
rxs0005 wrote:
Larry, Michael, and Doug have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?

(A) 21
(B) 42
(C) 120
(D) 504
(E) 5040


Consider this: we have 5 donuts d and 2 separators |, like: ddddd||. How many permutations (arrangements) of these symbols are possible? Total of 7 symbols (5+2=7), out of which 5 d's and 2 |'s are identical, so \frac{7!}{5!2!}=21.

We'll get combinations like: dd|d|dd this would mean that Larry got 2 donuts, Michael got 1 donut and Doug got 2 donuts, so to the left of the first separator are Larry's donuts, between the separators are Michael's donuts and to the right of the second separator are Doug's donuts

Answer: A.

This can be done with direct formula as well:

The total number of ways of dividing n identical items (5 donuts in our case) among r persons or objects (3 persons in our case), each one of whom, can receive 0, 1, 2 or more items (from zero to 5 in our case) is {n+r-1}_C_{r-1}.

In our case we'll get: {n+r-1}_C_{r-1}={5+3-1}_C_{3-1}={7}C2=\frac{7!}{5!2!}=21.

Similar question: integers-less-than-85291.html#p710836
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23351
Followers: 3604

Kudos [?]: 28710 [1] , given: 2815

Re: Larry, Michael, and Doug have five donuts to share. If any [#permalink] New post 05 Jul 2014, 06:09
1
This post received
KUDOS
Expert's post
deya wrote:
Dear Bunuel,

Thanks for the great explanation. But there is a catch that is not clear to me. I read all other similar types of questions and also went through the explanations given by you. There you have used 3 separators for all the cases but here you have used 2. Could you tell me how would I know that how many separators should I use.

Thanks in advance. :-D


Distributing between 4 use 3 separators;
Distributing between 3 use 2 separators.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Director
Director
avatar
Status: -=GMAT Jedi=-
Joined: 04 Jan 2011
Posts: 740
Location: Kochi, India
Schools: ISB
WE 1: Engineer - Larsen & Toubro, ECC Division
WE 2: Faculty - T.I.M.E.
Followers: 33

Kudos [?]: 130 [0], given: 66

Re: Combinations tough [#permalink] New post 04 Feb 2011, 17:46
Nice! Thanks man :)
_________________

Mission: Be a force of good and make a positive difference to every life I touch!

From 650 to 710 to 750 - My Tryst With GMAT [Experience Thread]

Manager
Manager
avatar
Joined: 02 Jan 2013
Posts: 53
GMAT 1: 750 Q51 V40
WE: Consulting (Consulting)
Followers: 0

Kudos [?]: 35 [0], given: 1

Larry, Michael, and Doug have five donuts to share. If any one o [#permalink] New post 17 Jan 2013, 08:17
Another awesome variation to this question (the one mentioned above) would be:

How many integer solutions (x,y,z) are there to the equation: x+y+z = 20, where x is at least equal to 3, y is at least equal to 4, and z is at least equal to 5
_________________

Please press "kudo" if this helped you!

Manager
Manager
avatar
Joined: 18 Oct 2011
Posts: 92
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Followers: 2

Kudos [?]: 24 [0], given: 0

Re: Larry, Michael, and Doug have five donuts to share. If any [#permalink] New post 17 Jan 2013, 10:56
should it not state identical donuts to share? relatively straightforward question but got confused as to whether we needed to use combinations formula and then arrange between the 3 people
Manager
Manager
avatar
Joined: 06 Feb 2013
Posts: 60
Followers: 1

Kudos [?]: 10 [0], given: 33

Re: Combinations tough [#permalink] New post 03 Sep 2013, 07:05
Bunuel wrote:
rxs0005 wrote:
Larry, Michael, and Doug have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?

(A) 21
(B) 42
(C) 120
(D) 504
(E) 5040


Consider this: we have 5 donuts d and 2 separators |, like: ddddd||. How many permutations (arrangements) of these symbols are possible? Total of 7 symbols (5+2=7), out of which 5 d's and 2 |'s are identical, so \frac{7!}{5!2!}=21.

We'll get combinations like: dd|d|dd this would mean that Larry got 2 donuts, Michael got 1 donut and Doug got 2 donuts, so to the left of the first separator are Larry's donuts, between the separators are Michael's donuts and to the right of the second separator are Doug's donuts

Answer: A.

This can be done with direct formula as well:

The total number of ways of dividing n identical items (5 donuts in our case) among r persons or objects (3 persons in our case), each one of whom, can receive 0, 1, 2 or more items (from zero to 5 in our case) is {n+r-1}_C_{r-1}.

In our case we'll get: {n+r-1}_C_{r-1}={5+3-1}_C_{3-1}={7}C2=\frac{7!}{5!2!}=21.

Similar question: integers-less-than-85291.html#p710836


Bunuel - could you explain how this problem would sound if I used a simple counting principle like Larry can get 5 doughnuts Michael 4...all the way to have 5! and therefore I would get 5!= 120, which would obviously be too easy but I am a little confused as to the difference in wording. Solution and those dividers make good sense, so thanks for that.
_________________

There are times when I do not mind kudos...I do enjoy giving some for help

Intern
Intern
avatar
Joined: 19 Apr 2013
Posts: 25
Followers: 0

Kudos [?]: 0 [0], given: 57

Larry, Michael, and Doug have five donuts to share [#permalink] New post 29 Sep 2013, 02:08
Hi Guys,

Please help me with this question and explain the logic used.

Thanks.
Attachments

Untitled.jpg
Untitled.jpg [ 37.01 KiB | Viewed 1907 times ]

Expert Post
Moderator
Moderator
User avatar
Status: It always seems impossible until it's done!!
Joined: 29 Aug 2012
Posts: 423
Location: India
Followers: 22

Kudos [?]: 333 [0], given: 130

GMAT ToolKit User Premium Member CAT Tests
Re: Larry, Michael, and Doug have five donuts to share [#permalink] New post 29 Sep 2013, 02:46
Expert's post
PrateekDua wrote:
Hi Guys,

Please help me with this question and explain the logic used.

Thanks.


Hi, This is already discussed :-D ,

Anyways please find the detail solution and discussion here combinatorics-ii-82046.html 8-) ..
_________________

Believe you can and you're halfway there- Theodore Roosevelt


Rules for posting in Quants Forum || Rules for posting in verbal forum

Improving from V30 to V40 | Improving from Q35-40 to Q47 | Bunuel Special Problem Collections New!!


Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23351
Followers: 3604

Kudos [?]: 28710 [0], given: 2815

Re: Larry, Michael, and Doug have five donuts to share [#permalink] New post 29 Sep 2013, 09:56
Expert's post
PrateekDua wrote:
Hi Guys,

Please help me with this question and explain the logic used.

Thanks.


Merging similar topics. Please refer to the solutions above.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule 6. Thank you.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 23 May 2013
Posts: 51
Concentration: Finance, Social Entrepreneurship
GMAT Date: 11-25-2013
Followers: 0

Kudos [?]: 13 [0], given: 17

Re: Larry, Michael, and Doug have five donuts to share. If any [#permalink] New post 05 Mar 2014, 10:51
If you get confused about combinations, there's a simple way to count these combinations as well, by counting the number of ways 5 can be summed with 3 numbers.

{5,0,0} = 3 possibilities.
{4,1,0} = 6 possibilities.
{3,2,0} = 6 possibilities.
{3,1,1} = 3 possibilities.
{2,2,1} = 3 possibilities.
Total = 21 possibilities.

Tip: For each set, we only have to consider numbers less than the first; for instance, we wouldn't consider {2,3,0} because that's already accounted for in a permutation of {3,2,0}
Intern
Intern
avatar
Joined: 12 Sep 2012
Posts: 19
Followers: 0

Kudos [?]: 1 [0], given: 9

Re: Larry, Michael, and Doug have five donuts to share. If any [#permalink] New post 03 Jul 2014, 08:07
Dear Bunuel,

Thanks for the great explanation. But there is a catch that is not clear to me. I read all other similar types of questions and also went through the explanations given by you. There you have used 3 separators for all the cases but here you have used 2. Could you tell me how would I know that how many separators should I use.

Thanks in advance. :-D
Intern
Intern
avatar
Joined: 18 Jun 2014
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 222

Re: Larry, Michael, and Doug have five donuts to share. If any [#permalink] New post 06 Jul 2014, 04:50
Why 3^5 is not a correct answer?
Considering each donut has 3 possibilities(L,M &D)...
Kindly regards
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23351
Followers: 3604

Kudos [?]: 28710 [0], given: 2815

Re: Larry, Michael, and Doug have five donuts to share. If any [#permalink] New post 06 Jul 2014, 09:29
Expert's post
1
This post was
BOOKMARKED
Re: Larry, Michael, and Doug have five donuts to share. If any   [#permalink] 06 Jul 2014, 09:29
    Similar topics Author Replies Last post
Similar
Topics:
Larry, Michael, and Doug have five donuts to share PrateekDua 0 29 Sep 2013, 02:46
2 Experts publish their posts in the topic Any golden rule pls share ypriyankha 5 18 Aug 2010, 13:23
Larry, Michael, and Doug have five donuts to share. If any AK 7 28 Dec 2006, 22:31
Five students Joe, Katy, Lori, Michael and Natasha must minhthel 6 23 Jul 2006, 00:08
1 Larry, Michael, and Doug have five donuts to share. If any saha 3 19 May 2006, 22:22
Display posts from previous: Sort by

Larry, Michael, and Doug have five donuts to share. If any

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.