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

It is currently 03 Aug 2020, 10:17

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

3 dwarves and 3 Elves sit down in a row of 6 chairs. If no

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Senior Manager
Senior Manager
User avatar
Joined: 26 Mar 2006
Posts: 266
3 dwarves and 3 Elves sit down in a row of 6 chairs. If no  [#permalink]

Show Tags

New post 28 Dec 2007, 10:41
5
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (01:10) correct 0% (00:00) wrong based on 22 sessions

HideShow timer Statistics

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

I feel the approach in MGMAT for this problem is not the best ... :roll: So I am looking for alternatives...Thanks..

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.


If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Manager
Manager
User avatar
Joined: 01 Sep 2006
Posts: 201
Location: Phoenix, AZ, USA
Re: Combinatorics - Dwarf and Elves  [#permalink]

Show Tags

New post 28 Dec 2007, 10:46
Beyond700 wrote:
3 dwarves and 3 Elves sit down in a row of 6 chairs. If no dwarf will sit next to another dwarf and no elf will sit next to another elf, in how many different ways can the elves and dwarves sit?

I feel the approach in MGMAT for this problem is not the best ... :roll: So I am looking for alternatives...Thanks..


S S S S S S
D E D E D E Possible seat for D 3C1=3 Possible seat for E 3C1=3 9 ways
E D E D E D same result 9

Total 18 ways
CEO
CEO
User avatar
B
Joined: 17 Nov 2007
Posts: 2913
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
GMAT ToolKit User
  [#permalink]

Show Tags

New post 28 Dec 2007, 10:51
5
1
72

dedede: N1=3P3*3P3=6*6=36
ededed: N2=3P3*3P3=6*6=36

3P3 - 3 different things at 3 different positions.

N=36*2=72
Senior Manager
Senior Manager
User avatar
Joined: 26 Mar 2006
Posts: 266
  [#permalink]

Show Tags

New post 28 Dec 2007, 11:09
4
walker wrote:
72

dedede: N1=3P3*3P3=6*6=36
ededed: N2=3P3*3P3=6*6=36

3P3 - 3 different things at 3 different positions.

N=36*2=72


Bulls eye....

But I did this in this way (simple layman terms)

'Chairs ' - 1 2 3 4 5 6
possibile - 6*3*2*2*1*1 = 72

The good thing is that I managed to solve 4 to 5 such questions and but I am not sure how efficient this approach will be.. Any comments...

MGMAT has 1/2 page solution for this problem...
CEO
CEO
User avatar
B
Joined: 17 Nov 2007
Posts: 2913
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
GMAT ToolKit User
  [#permalink]

Show Tags

New post 28 Dec 2007, 11:44
Beyond700 wrote:
The good thing is that I managed to solve 4 to 5 such questions and but I am not sure how efficient this approach will be.. Any comments...


maybe this will be useful: http://www.gmatclub.com/forum/t56486

I think it is not a good idea to use only one approach for combination-permutation-probability problems.
I have a few general principles that seems be helpful for me in CPP problems.

1. try to find a answer by several ways.
2. use pattern approach for enumeration of possibilities for problems with complex restrictions.
Manager
Manager
avatar
Joined: 27 Oct 2008
Posts: 125
Re: Combinatorics - Dwarf and Elves  [#permalink]

Show Tags

New post 27 Sep 2009, 10:26
2
3 dwarves and 3 Elves sit down in a row of 6 chairs. If no dwarf will sit next to another dwarf and no elf will sit next to another elf, in how many different ways can the elves and dwarves sit?

Soln:
Assuming the Dwarves taken 1st , 3rd and 5th place. The other 3 places will be taken by Elves.
Hence total number of arrangements = 3! * 3!

Now if Dwarves take 2nd, 4th and 6th place. The other 3 places will be taken by Elves.
Hence total number of arrangements = 3! * 3!

Thus total number of ways is = 3! * 3! + 3! * 3! = 72 ways
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15595
Re: 3 dwarves and 3 Elves sit down in a row of 6 chairs. If no  [#permalink]

Show Tags

New post 14 Mar 2019, 01:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: 3 dwarves and 3 Elves sit down in a row of 6 chairs. If no   [#permalink] 14 Mar 2019, 01:34

3 dwarves and 3 Elves sit down in a row of 6 chairs. If no

  Question banks Downloads My Bookmarks Reviews Important topics  





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