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

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Senior Manager
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At a dinner party, 5 people ar eto be seated around a [#permalink]

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New post 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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Re: Combinatorics from GMATPrep [#permalink]

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

First confirm it..

Thanks

Vishal Shah

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Re: Combinatorics from GMATPrep [#permalink]

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New post 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

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Re: Combinatorics from GMATPrep [#permalink]

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New post 22 Sep 2008, 07:25
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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

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Re: Combinatorics from GMATPrep [#permalink]

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New post 23 Sep 2008, 00:15
OA is 24.

I could not solve this, but it was fairly easy to guess.
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Re: Combinatorics from GMATPrep [#permalink]

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New post 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.

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Re: Combinatorics from GMATPrep [#permalink]

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New post 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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Re: Combinatorics from GMATPrep [#permalink]

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New post 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?

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Re: Combinatorics from GMATPrep [#permalink]

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New post 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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