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# At a dinner party 5 people are to be seated around a circula

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Intern
Joined: 20 May 2012
Posts: 20
At a dinner party 5 people are to be seated around a circula [#permalink]

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23 Mar 2013, 21:36
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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
[Reveal] Spoiler: OA
Manager
Joined: 27 Jan 2013
Posts: 229
GMAT 1: 780 Q49 V51
Re: At a dinner party 5 people are to be seated around a circula [#permalink]

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23 Mar 2013, 22:00
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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

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If you found my post useful KUDOS are much appreciated.

Here is the first set along with some strategies for approaching this work: http://gmatclub.com/forum/the-economist-reading-comprehension-challenge-151479.html

Math Expert
Joined: 02 Sep 2009
Posts: 44566
Re: At a dinner party 5 people are to be seated around a circula [#permalink]

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24 Mar 2013, 02:21
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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:

$$R = \frac{n!}{n} = (n-1)!$$"

$$(n-1)!=(5-1)!=24$$

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Hope it helps.
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Intern
Joined: 20 May 2012
Posts: 20
Re: At a dinner party 5 people are to be seated around a circula [#permalink]

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24 Mar 2013, 08:55
HerrGrau wrote:
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.

Thank you so much HG!

This was a very simple and concise explanation! SO if there were 10 people seated at the circular table, we would solve it as 10!/10?

Thanks once again!
Manager
Joined: 27 Jan 2013
Posts: 229
GMAT 1: 780 Q49 V51
Re: At a dinner party 5 people are to be seated around a circula [#permalink]

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24 Mar 2013, 12:34
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

GMAT vs GRE Comparison

If you found my post useful KUDOS are much appreciated.

Here is the first set along with some strategies for approaching this work: http://gmatclub.com/forum/the-economist-reading-comprehension-challenge-151479.html

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Joined: 16 Oct 2010
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Location: Pune, India
Re: At a dinner party 5 people are to be seated around a circula [#permalink]

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24 Mar 2013, 22:01
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"
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 07 Feb 2011 Posts: 102 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' _________________ We appreciate your kudos' Senior Manager Joined: 15 Aug 2013 Posts: 276 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? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8024 Location: Pune, India 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: http://www.veritasprep.com/blog/2011/10 ... angements/ http://www.veritasprep.com/blog/2011/10 ... ts-part-i/ http://www.veritasprep.com/blog/2011/11 ... 3-part-ii/ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: At a dinner party 5 people are to be seated around a circula [#permalink]

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01 Mar 2018, 18:37
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

When determining the number way to arrange a group around a circle, we subtract 1 from the total and set it to a factorial. Thus, the total number of possible sitting arrangements for 5 people around a circular table is 4! = 24.

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Re: At a dinner party 5 people are to be seated around a circula   [#permalink] 01 Mar 2018, 18:37
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