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

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At a dinner party 5 people are to be seated around a circula [#permalink] New post 23 Mar 2013, 20:36
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78% (01:27) correct 21% (00:47) wrong based on 32 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?

A. 5
B. 10
C. 24
D. 32
E. 120
[Reveal] Spoiler: OA
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Re: At a dinner party 5 people are to be seated around a circula [#permalink] New post 23 Mar 2013, 21:00
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Expert's post
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.
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4th set of the Economist Reading Comprehension Challenge: http://gmatclub.com/forum/the-economist-reading-comprehension-challenge-156334.html

5th set of the Economist Reading Comprehension Challenge: http://gmatclub.com/forum/economist-reading-comprehension-challenge-156893.html

6th set of the Economist Reading Comprehension Challenge: http://gmatclub.com/forum/economist-reading-comprehension-challenge-157575.html

7th set of the Economist Reading Comprehension Challenge: http://atlanticgmat.com/economist-reading-comprehension-challenge-7/

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Re: At a dinner party 5 people are to be seated around a circula [#permalink] New post 24 Mar 2013, 01:21
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


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

Answer: C.

Questions about this concept to practice:
seven-men-and-seven-women-have-to-sit-around-a-circular-92402.html
a-group-of-four-women-and-three-men-have-tickets-for-seven-a-88604.html
the-number-of-ways-in-which-5-men-and-6-women-can-be-seated-94915.html
in-how-many-different-ways-can-4-ladies-and-4-gentlemen-be-102187.html
4-couples-are-seating-at-a-round-tables-how-many-ways-can-131048.html
at-a-party-5-people-are-to-be-seated-around-a-circular-104101.html
seven-family-members-are-seated-around-their-circular-dinner-102184.html
seven-men-and-seven-women-have-to-sit-around-a-circular-11473.html
a-group-of-8-friends-sit-together-in-a-circle-alice-betty-106928.html
seven-men-and-five-women-have-to-sit-around-a-circular-table-98185.html
a-group-of-8-friends-sit-together-in-a-circle-alice-betty-106928.html
find-the-number-of-ways-in-which-four-men-two-women-and-a-106919.html
gmat-club-monday-giveaway-155157.html (700+)

Hope it helps.
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Re: At a dinner party 5 people are to be seated around a circula [#permalink] New post 24 Mar 2013, 01:58
I am a little weak in combinatorics , could some one explain to be why the answer is not 5! .
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Re: At a dinner party 5 people are to be seated around a circula [#permalink] New post 24 Mar 2013, 02:00
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Re: At a dinner party 5 people are to be seated around a circula [#permalink] New post 24 Mar 2013, 07:55
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!
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Re: At a dinner party 5 people are to be seated around a circula [#permalink] New post 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.
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"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 Blog and Tutoring: http://www.AtlanticGMAT.com

If you found my post useful KUDOS are much appreciated.

IMPROVE YOUR READING COMPREHENSION with the ECONOMIST READING COMPREHENSION CHALLENGE:

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

2nd set of the Economist Reading Comprehension Challenge: http://gmatclub.com/forum/the-economist-reading-comprehension-challenge-151827.html

3rd set of the Economist Reading Comprehension Challenge: http://gmatclub.com/forum/the-economist-reading-comprehension-challenge-152565.html

4th set of the Economist Reading Comprehension Challenge: http://gmatclub.com/forum/the-economist-reading-comprehension-challenge-156334.html

5th set of the Economist Reading Comprehension Challenge: http://gmatclub.com/forum/economist-reading-comprehension-challenge-156893.html

6th set of the Economist Reading Comprehension Challenge: http://gmatclub.com/forum/economist-reading-comprehension-challenge-157575.html

7th set of the Economist Reading Comprehension Challenge: http://atlanticgmat.com/economist-reading-comprehension-challenge-7/

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Re: At a dinner party 5 people are to be seated around a circula [#permalink] New post 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"
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Re: At a dinner party 5 people are to be seated around a circula [#permalink] New post 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'
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Re: At a dinner party 5 people are to be seated around a circula   [#permalink] 25 Mar 2013, 02:03
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