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]

Show Tags

23 Mar 2013, 21:36

2

This post received KUDOS

5

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

15% (low)

Question Stats:

69% (01:22) correct
31% (00:32) wrong based on 185 sessions

HideShow timer Statistics

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]

Show Tags

23 Mar 2013, 22:00

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]

Show Tags

24 Mar 2013, 02:21

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]

Show Tags

24 Mar 2013, 12:34

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]

Show Tags

24 Mar 2013, 22:01

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]

Show Tags

25 Mar 2013, 03:03

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]

Show Tags

23 Apr 2014, 19:41

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]

Show Tags

23 Apr 2014, 20:18

1

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

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]

Show Tags

01 Sep 2015, 20:08

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]

Show Tags

01 Sep 2015, 22:06

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.

Excellent posts dLo saw your blog too..!! Man .. you have got some writing skills. And Just to make an argument = You had such an amazing resume ; i am glad...

So Much $$$ Business school costs a lot. This is obvious, whether you are a full-ride scholarship student or are paying fully out-of-pocket. Aside from the (constantly rising)...