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.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
At a dinner party 5 people are to be seated around a circula [#permalink]
23 Mar 2013, 20:36
2
This post received KUDOS
4
This post was BOOKMARKED
00:00
A
B
C
D
E
Difficulty:
15% (low)
Question Stats:
68% (01:22) correct
32% (00:33) wrong based on 171 sessions
At a dinner party 5 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other.What is the total number of possible sitting arrangements or the group?
Re: At a dinner party 5 people are to be seated around a circula [#permalink]
23 Mar 2013, 21:00
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
Hi there,
You can treat this as an ordering question except that for a circular arrangement you need to divide by the number of spaces. So in this case:
5!/5=24
If you spin the circle to right, that doesn't count as a new arrangement. Dividing by the number of spaces takes that into consideration.
Happy Studies,
HG. _________________
"It is a curious property of research activity that after the problem has been solved the solution seems obvious. This is true not only for those who have not previously been acquainted with the problem, but also for those who have worked over it for years." -Dr. Edwin Land
Re: At a dinner party 5 people are to be seated around a circula [#permalink]
24 Mar 2013, 01:21
Expert's post
5
This post was BOOKMARKED
Val1986 wrote:
At a dinner party 5 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other.What is the total number of possible sitting arrangements or the group?
A. 5 B. 10 C. 24 D. 32 E. 120
We have a case of circular arrangement.
The number of arrangements of n distinct objects in a row is given by \(n!\). The number of arrangements of n distinct objects in a circle is given by \((n-1)!\).
From Gmat Club Math Book (combinatorics chapter): "The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:
Re: At a dinner party 5 people are to be seated around a circula [#permalink]
24 Mar 2013, 11:34
Expert's post
You are very welcome. Yes, 10!/10 is exactly right for 10 people around a circular table.
HG. _________________
"It is a curious property of research activity that after the problem has been solved the solution seems obvious. This is true not only for those who have not previously been acquainted with the problem, but also for those who have worked over it for years." -Dr. Edwin Land
Re: At a dinner party 5 people are to be seated around a circula [#permalink]
24 Mar 2013, 21:01
Expert's post
Val1986 wrote:
At a dinner party 5 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other.What is the total number of possible sitting arrangements or the group?
A. 5 B. 10 C. 24 D. 32 E. 120
Check out this post on circular arrangements. It discusses why the number of arrangements is n!/n (which is the same as (n-1)!) in case there are n people sitting around a round table. http://www.veritasprep.com/blog/2011/10 ... angements/
It also discusses the relevance of this statement in the question: "Two sitting arrangements are considered different only when the positions of the people are different relative to each other" _________________
Re: At a dinner party 5 people are to be seated around a circula [#permalink]
25 Mar 2013, 02:03
shelrod007 wrote:
I am a little weak in combinatorics , could some one explain to be why the answer is not 5! .
The short answer would be something like this to your question rephrased (why isn't it n! instead of n-1! ?)
The reason is that RELATIVE to each other, ie (BAC) (CAB) ie BA AB CA AC, are seated next to each other and can be considered 'one group' _________________
Re: At a dinner party 5 people are to be seated around a circula [#permalink]
23 Apr 2014, 18:41
VeritasPrepKarishma wrote:
Val1986 wrote:
At a dinner party 5 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other.What is the total number of possible sitting arrangements or the group?
A. 5 B. 10 C. 24 D. 32 E. 120
Check out this post on circular arrangements. It discusses why the number of arrangements is n!/n (which is the same as (n-1)!) in case there are n people sitting around a round table. http://www.veritasprep.com/blog/2011/10 ... angements/
It also discusses the relevance of this statement in the question: "Two sitting arrangements are considered different only when the positions of the people are different relative to each other"
Hi Karishma,
If there were constraints such as A can't be next to B or C, does that mean that we now have 5 seats but since 3 of them are fixed, the solution would be 2!/2?
Re: At a dinner party 5 people are to be seated around a circula [#permalink]
23 Apr 2014, 19:18
1
This post received KUDOS
Expert's post
russ9 wrote:
Hi Karishma,
If there were constraints such as A can't be next to B or C, does that mean that we now have 5 seats but since 3 of them are fixed, the solution would be 2!/2?
I am assuming your question is this: 5 people are to be seated around a circular table such that A sits neither next to B nor next to C. How many arrangements are possible?
I don't know how you consider "...3 of them are fixed".
The way you handle this constraint would be this:
There are 5 vacant seats. Make A occupy 1 seat in 1 way (because all seats are same before anybody sits). Now we have 4 unique vacant seats (unique with respect to A) and 4 people. B and C cannot sit next to A so D and E occupy the seats right next to A on either side. This can be done in 2! ways: D A E or E A D
B and C occupy the two unique seats away from A. This can be done in 2! ways.
Total number of arrangements = 2! * 2! = 4
Check out these posts. First discusses theory of circular arrangements and next two discuss circular arrangements with various constraints:
At a dinner party 5 ppl are to seated around a circular table [#permalink]
01 Sep 2015, 19:08
At a dinner party 5 ppl are to seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of possible seating arrangements for the people.
Re: At a dinner party 5 people are to be seated around a circula [#permalink]
01 Sep 2015, 21:06
Expert's post
dotty2504 wrote:
At a dinner party 5 ppl are to seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of possible seating arrangements for the people.
A.5 B.10 C.24 D.32 E.120
Merging topics. Please refer to the discussion above.
You know what’s worse than getting a ding at one of your dreams schools . Yes its getting that horrid wait-listed email . This limbo is frustrating as hell . Somewhere...
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Wow! MBA life is hectic indeed. Time flies by. It is hard to keep track of the time. Last week was high intense training Yeah, Finance, Accounting, Marketing, Economics...