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# At a dinner party, 5 people ar eto be seated around a

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Senior Manager
Joined: 16 Jul 2008
Posts: 285
At a dinner party, 5 people ar eto be seated around a [#permalink]

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22 Sep 2008, 06:04
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

At a dinner party, 5 people ar eto be seated around a circular table. two seating arrangement are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?

5

10

24

32

120
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Manager
Joined: 22 Sep 2008
Posts: 119

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22 Sep 2008, 07:00
I think answer should be 10.

First confirm it..

Thanks

Vishal Shah
Director
Joined: 14 Aug 2007
Posts: 704

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22 Sep 2008, 07:20
Nerdboy wrote:
At a dinner party, 5 people ar eto be seated around a circular table. two seating arrangement are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?

5

10

24

32

120

5 people: circular arrangement = 4! = 24 C
Director
Joined: 12 Jul 2008
Posts: 513
Schools: Wharton

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22 Sep 2008, 07:25
1
KUDOS
Nerdboy wrote:
At a dinner party, 5 people ar eto be seated around a circular table. two seating arrangement are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?

5

10

24

32

120

Two ways to do this:
Number of ways to arrange 5 people = 5!
Number of ways to arrange one permutation around a circular table = 5

Number of total seating possibilities = 5!/5 = 24

OR

Fix one person in a seat and everyone else sits relative to that one person.
Number of ways to arrange 4 people = 4! = 24
Senior Manager
Joined: 16 Jul 2008
Posts: 285

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23 Sep 2008, 00:15
OA is 24.

I could not solve this, but it was fairly easy to guess.
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Manager
Joined: 02 Aug 2007
Posts: 221
Schools: Life

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16 Feb 2009, 22:30
Nerdboy wrote:
At a dinner party, 5 people ar eto be seated around a circular table. two seating arrangement are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?

5

10

24

32

120

I got (5-1)! = 24
I don't get the part in bold, how does it affect the solution?
Thanks.
CEO
Joined: 21 Jan 2007
Posts: 2713
Location: New York City

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17 Feb 2009, 02:22
xALIx wrote:
Nerdboy wrote:
At a dinner party, 5 people ar eto be seated around a circular table. two seating arrangement are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?

5

10

24

32

120

I got (5-1)! = 24
I don't get the part in bold, how does it affect the solution?
Thanks.

it clarifies that it is a circular permutation in that AB is the same as BA.
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Manager
Joined: 02 Aug 2007
Posts: 221
Schools: Life

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17 Feb 2009, 11:57
bmwhype2 wrote:
it clarifies that it is a circular permutation in that AB is the same as BA.

I thought it meant that AB and BA are different setups, which is inline with the concept of circular permutation. Check this out
http://mathworld.wolfram.com/CircularPermutation.html

Am I off?
SVP
Joined: 07 Nov 2007
Posts: 1765
Location: New York

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17 Feb 2009, 12:04
xALIx wrote:
bmwhype2 wrote:
it clarifies that it is a circular permutation in that AB is the same as BA.

I thought it meant that AB and BA are different setups, which is inline with the concept of circular permutation. Check this out
http://mathworld.wolfram.com/CircularPermutation.html

Am I off?

e.g
take you have only 3 persons 1,2,3 .

123 -- 312 -- 231 -- are same..
132 -- 213 -- 321 -- are same..

only these two possibilities = 3-1 ! = 2! =2

if there are only two person (A and B)

AB is same as BA.

2-1! =1 way.
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Re: Combinatorics from GMATPrep   [#permalink] 17 Feb 2009, 12:04
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# At a dinner party, 5 people ar eto be seated around a

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