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

It is currently 17 Sep 2014, 05:43

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

Three dwarves and three elves sit down in a row of six

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
avatar
Joined: 10 Nov 2010
Posts: 268
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
Followers: 5

Kudos [?]: 49 [0], given: 22

GMAT Tests User
Three dwarves and three elves sit down in a row of six [#permalink] New post 16 Feb 2011, 12:13
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (01:25) correct 0% (00:00) wrong based on 2 sessions
Three dwarves and three elves sit down in a row of six chairs. If no dwarf will sit next to another dwarf and no elf wil sit next to another elf, in how many different ways can the elves and dwarves sit?


as per my solution

on first chair from 3dwarves any one can sit on another chair from 3elves any one can sit nd so on

3*3*2*2*1*1=36

But OA is
[Reveal] Spoiler:
72

_________________

The proof of understanding is the ability to explain it.


Last edited by Bunuel on 28 Feb 2012, 13:07, edited 2 times in total.
Edited the question
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29662
Followers: 3494

Kudos [?]: 26262 [1] , given: 2708

Re: arrangements made [#permalink] New post 16 Feb 2011, 12:27
1
This post received
KUDOS
Expert's post
Three dwarves and three elves sit down in a row of six chairs. If no dwarf will sit next to another dwarf and no elf wil sit next to another elf, in how many different ways can the elves and dwarves sit?

In order to meet the restriction dwarves and elves must sit either DEDEDE or EDEDED. There are 3!*3!=36 arrangements possible for each case (3! arrangements of dwarves and 3! arrangements of elves), so total ways to sit are 2*36=72.
_________________

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

Senior Manager
Senior Manager
avatar
Status: Up again.
Joined: 31 Oct 2010
Posts: 493
Location: India
GMAT 1: 710 Q48 V40
WE: Project Management (Manufacturing)
Followers: 13

Kudos [?]: 54 [0], given: 74

Re: arrangements made [#permalink] New post 17 Feb 2011, 05:29
GMATD11 wrote:
Pls chk the image

as per my solution

on first chair from 3dwarves any one can sit on another chair from 3elves any one can sit nd so on

3*3*2*2*1*1=36

But OA is 72


You forgot to multiply the answer with 2. You see, either one the dwarves can take the first seat or one of the elves can take it. If a dwarf occupies the first seat, the other dwarves will sit on the 3rd and 5th seat. Elves will sit on 2nd, 4th and 6th seats. So as you have rightly calculated above, there will be 36 seating arrangements.

In the event where an elf takes the first seat, there will be as many combinations possible albeit the seats will change, with the elves taking the odd numbered seats and the dwarves taking the even numbered ones.

So total number of combinations= 36+36= 72.
_________________

My GMAT debrief: from-620-to-710-my-gmat-journey-114437.html

Current Student
User avatar
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 271
Location: Pakistan
Concentration: Strategy, Marketing
Schools: Insead '13 (M)
GMAT 1: 680 Q46 V37
GMAT 2: Q V
Followers: 24

Kudos [?]: 700 [0], given: 48

GMAT ToolKit User
elves [#permalink] New post 28 Feb 2012, 12:57
there are only two patterns: dedede, ededed. each will return same number of combinations.

combinations = 3*3*2*2*1*1*(2) = 72 ... multiply (2) because there are two patterns
_________________

press +1 Kudos to appreciate posts
Download Valuable Collection of Percentage Questions (PS/DS)

Intern
Intern
avatar
Joined: 05 Apr 2012
Posts: 43
Followers: 0

Kudos [?]: 8 [0], given: 12

combination [#permalink] New post 05 Apr 2012, 11:51
hello

IF 3 DWARFS AND THREE ELVES SIT DOWN IN A ROW OF 6 chairs . IF NO DWARFS WILL SIT NEXT TO ANOTHER DWARFS AND NO ELFS WILL SEAT NEXT TO ANOTHER ELFS
IN HOW MANY WAYS CAN THE ELVES AND DWARFS SIT?

answer to this practice exercises is 72
please explain your reasoning


thanks

best regards
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29662
Followers: 3494

Kudos [?]: 26262 [0], given: 2708

Re: combination [#permalink] New post 05 Apr 2012, 12:09
Expert's post
keiraria wrote:
hello

IF 3 DWARFS AND THREE ELVES SIT DOWN IN A ROW OF 6 chairs . IF NO DWARFS WILL SIT NEXT TO ANOTHER DWARFS AND NO ELFS WILL SEAT NEXT TO ANOTHER ELFS
IN HOW MANY WAYS CAN THE ELVES AND DWARFS SIT?

answer to this practice exercises is 72
please explain your reasoning


thanks

best regards


Merging similar topics. Please ask if anything remains unclear.

P.S. Please turn Caps Lock off when posting.
_________________

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

Intern
Intern
avatar
Joined: 05 Apr 2012
Posts: 43
Followers: 0

Kudos [?]: 8 [0], given: 12

Re: combination [#permalink] New post 05 Apr 2012, 12:33
Bunuel wrote:
keiraria wrote:
hello

IF 3 DWARFS AND THREE ELVES SIT DOWN IN A ROW OF 6 chairs . IF NO DWARFS WILL SIT NEXT TO ANOTHER DWARFS AND NO ELFS WILL SEAT NEXT TO ANOTHER ELFS
IN HOW MANY WAYS CAN THE ELVES AND DWARFS SIT?

answer to this practice exercises is 72
please explain your reasoning


thanks

best regards


Merging similar topics. Please ask if anything remains unclear.

P.S. Please turn Caps Lock off when posting.


Thanks my approach was the total number of way the 6 could sit minus the number of way the dwarf and the elfs can sit together
6!-3!x3!

i dont understand my mistake
best regards
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29662
Followers: 3494

Kudos [?]: 26262 [0], given: 2708

Re: combination [#permalink] New post 05 Apr 2012, 15:57
Expert's post
keiraria wrote:
Bunuel wrote:
keiraria wrote:
hello

IF 3 DWARFS AND THREE ELVES SIT DOWN IN A ROW OF 6 chairs . IF NO DWARFS WILL SIT NEXT TO ANOTHER DWARFS AND NO ELFS WILL SEAT NEXT TO ANOTHER ELFS
IN HOW MANY WAYS CAN THE ELVES AND DWARFS SIT?

answer to this practice exercises is 72
please explain your reasoning


thanks

best regards


Merging similar topics. Please ask if anything remains unclear.

P.S. Please turn Caps Lock off when posting.


Thanks my approach was the total number of way the 6 could sit minus the number of way the dwarf and the elfs can sit together
6!-3!x3!

i dont understand my mistake
best regards


The problem with that solution is that 3!*3! does not give you all cases when dwarves and elves sit together. 3!*3! counts only the cases when all 3 dwarves and all 3 elves are sitting together for example all cases for DDDEEE. But since we are asked to find the ways to arrange them so that no dwarf will sit next to another dwarf and no elf wil sit next to another elf then there are many other cases possible when this condition is violated: EEEDDD, EEDDED, DDEEDE, ...
_________________

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: 13 Oct 2012
Posts: 78
Concentration: General Management, Leadership
Schools: IE '15 (A)
GMAT 1: 760 Q49 V46
Followers: 1

Kudos [?]: -15 [0], given: 0

Three dwarves and three elves sit down in a row of six chairs. I [#permalink] New post 07 Jan 2013, 10:51
ededed OR dedede
3*3*2*2*1*1 + 3*3*2*2*1*1
= 72
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: 3 dwarves and 3 Elves sit down in a row of 6 chairs. If no [#permalink] New post 07 Jan 2013, 10:56
you can either have the following arragements of seating positions
EDEDED or DEDEDE

Therefore for the first arragement you would have 3!x3! ways to sit the 6 people. Since there are two possible seating arragememts you would have 2(3!x3!) = 72
Manager
Manager
User avatar
Joined: 07 Feb 2011
Posts: 89
Followers: 0

Kudos [?]: 17 [0], given: 43

Three dwarves and three elves sit down in a row of six chairs. I [#permalink] New post 22 Jan 2013, 02:34
How would we do this using COMBINATIONS/C as opposed to permutations or just counting out possibilities for each of the 6 slots (ie 6x3x2x2)?
_________________

We appreciate your kudos'

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4766
Location: Pune, India
Followers: 1112

Kudos [?]: 5040 [0], given: 164

Re: Three dwarves and three elves sit down in a row of six chair [#permalink] New post 22 Jan 2013, 20:17
Expert's post
manimgoindowndown wrote:
How would we do this using COMBINATIONS/C as opposed to permutations or just counting out possibilities for each of the 6 slots (ie 6x3x2x2)?


You need to arrange the 6 people in 6 places. You can think in terms of combinations in the following way:

For the first chair, we select any one person of the 6 in 6C1 ways.
For the second chair, we select any one from the 3 in 3C1 ways (e.g. if an elf is sitting on the first chair, we need to choose out of the 3 dwarves only)
For the third chair, we select one of the leftover 2 (e.g. one elf is already sitting in first chair) in 2C1 ways
For the fourth chair, we select one of the leftover 2 (e.g. one dwarf is already sitting in the second chair and we need to choose of the remaining 2) in 2C1 ways
For the fifth and sixth chairs, there is only one choice each.

Answer: 6C1 * 3C1 * 2C1 * 2C1 = 6*3*2*2 = 72
(note that this is the basic counting principle itself. For more, check: http://www.veritasprep.com/blog/2011/10 ... inatorics/)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Intern
Intern
avatar
Joined: 29 Aug 2013
Posts: 4
Followers: 0

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

Permutation & Combination question [#permalink] New post 15 Dec 2013, 08:27
Hello forum,

how can you solve this question using either permutation or combination?

3 gnomes and 3 elves sit down in a row of 6 chairs. If no gnome will sit next to another gnome and no elf will sit next to another elf, in how many different ways can the elves and gnomes sit?


This is a question from one of the MGMAT books and their solutions does not mention a way to solve this by using either the formula for combination or permutation. I could not solve it on my own, so I would kindly ask you to help me with this.

Best
Expert Post
GMAT Pill Instructor
User avatar
Joined: 14 Apr 2009
Posts: 1559
Location: New York, NY
Followers: 288

Kudos [?]: 658 [0], given: 6

Re: Permutation & Combination question [#permalink] New post 15 Dec 2013, 18:49
Expert's post
You might break this down. At the highest level there's only 2 sets:

Seats #1, 2, 3, 4, 5, 6 would be:
Gnome, Elf, Gnome, Elf, Gnome, Elf

Since gnomes can't sit next to gnomes and elves can't sit next to elves, the only other alternative for seats would be:
Elf, Gnome, Elf, Gnome, Elf, Gnome

We did that by moving the gnome to seat #2. But moving it to seat #3 would be a repeat of the first set mentioned. So there's only 2.

Now we have 2 * (TBD)

For each of the 2 sets above, the gnomes can be arranged and the elves can be fixed in their position.
So just line gnome1, gnome2, gnome3 and then rearrange them.

That's 3P3 = 3! = 3*2 = 6
So if the elves are fixed, there are 6 gnome variations.

But wait...the elves can vary too:
They also can be 3P3 = 6 with the gnomes fixed in their position.

So do 6 * 6 = 36 variations

But wait...we had 2 arrangements in the very beginning. One where gnome was at the very beginning and another where gnome was in the #2 spot.

SO take 36 * 2= 72

72 arrangements: 2 sets of 6 variations on 6 variations



For more information on permutations/combinations, try this free lesson on permutations/combinations from GMAT Pill.
_________________


... and more


Image What's Inside GMAT Pill?

Zeke Lee, GMAT Pill Study Method (Study Less. Score More.)


GMAT Pill Reviews | GMAT PILL Free Practice Test

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29662
Followers: 3494

Kudos [?]: 26262 [0], given: 2708

Re: Permutation & Combination question [#permalink] New post 16 Dec 2013, 00:13
Expert's post
mott wrote:
Hello forum,

how can you solve this question using either permutation or combination?

3 gnomes and 3 elves sit down in a row of 6 chairs. If no gnome will sit next to another gnome and no elf will sit next to another elf, in how many different ways can the elves and gnomes sit?


This is a question from one of the MGMAT books and their solutions does not mention a way to solve this by using either the formula for combination or permutation. I could not solve it on my own, so I would kindly ask you to help me with this.

Best


Merging similar topics. Please ask if anything remains unclear.
_________________

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

Intern
Intern
avatar
Joined: 12 Aug 2014
Posts: 2
Followers: 0

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

Three dwarves and three elves sit down in a row of six [#permalink] New post 12 Aug 2014, 11:44
Bunuel wrote:
mott wrote:
Hello forum,

how can you solve this question using either permutation or combination?

3 gnomes and 3 elves sit down in a row of 6 chairs. If no gnome will sit next to another gnome and no elf will sit next to another elf, in how many different ways can the elves and gnomes sit?


This is a question from one of the MGMAT books and their solutions does not mention a way to solve this by using either the formula for combination or permutation. I could not solve it on my own, so I would kindly ask you to help me with this.

Best


Merging similar topics. Please ask if anything remains unclear.


I'm trying to solve this in manner similar to your previous post ("Greg, Marcia, Peter, Jan, Bobby and Cindy go to a movie and sit next to each other in 6 adjacent seats in the front row of the theater. If Marcia and Jan will not sit next to each other, in how many different arrangements"... I am unable to post the link). How would you apply the rule where you find the total # of arrangements and then subtract the # of violations?

Can you please explain the difference? I cannot seem to solve this question (dwarves & elves) like the previous one (movie seats).
Three dwarves and three elves sit down in a row of six   [#permalink] 12 Aug 2014, 11:44
    Similar topics Author Replies Last post
Similar
Topics:
3 If three students are made to sit in a row, then 6 dont have Anasthaesium 3 26 Dec 2011, 23:58
Experts publish their posts in the topic Three dwarfs and three eleves sit down in a row of sit jimmyjamesdonkey 6 27 Jan 2008, 13:31
5 Experts publish their posts in the topic 3 dwarves and 3 Elves sit down in a row of 6 chairs. If no Beyond700 5 28 Dec 2007, 10:41
Experts publish their posts in the topic Six boys and six girls sit in a row at random.Find the LM 2 22 Dec 2007, 21:04
2 Experts publish their posts in the topic Three dwarves and three elves sit down in in the row of six rlevochkin 7 19 Jan 2006, 12:06
Display posts from previous: Sort by

Three dwarves and three elves sit down in a row of six

  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®.