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# Statistics - Gmatprep

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Statistics - Gmatprep [#permalink]  30 Oct 2009, 12:26
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Hi guys,

Please could you help me with the following statistics problem? I am not sure how to solve. I though that answer would be E but they say it's C. Thank you.

At a dinner party, 5 people are to be 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 different possible seating arrangements for the group?
A. 5
B. 10
C. 24
D. 32
E. 120
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Re: Statistics - Gmatprep [#permalink]  30 Oct 2009, 13:44
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ralucaroman wrote:
Hi guys,

Please could you help me with the following statistics problem? I am not sure how to solve. I though that answer would be E but they say it's C. Thank you.

At a dinner party, 5 people are to be 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 different possible seating arrangements for the group?

A. 5
B. 10
C. 24
D. 32
E. 120

Thats true. Circular combination/permutation is different from the line/column combination/permutation problem.

If it were a line/column combination/permutation problem, the solution woul be : 5! = 120.

However it is a circular combination/permutation problem, the solution would be: 5!/5 = 24 becaue you need to keep 1 person static. For that, lets say A cannot move from his place and next to him you can put 4 people. Then 3, then 2 and 1. So the no. of ways 5 people can be seated arround a circular table is 4! = 24.
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Re: Statistics - Gmatprep [#permalink]  30 Oct 2009, 18:26
Thank you. I understand it know.
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Re: Statistics - Gmatprep [#permalink]  30 Oct 2009, 19:10
[quote="ralucaroman"]

Two seating arrangements are considered different only when the positions of the people are different relative to each other.

What does this sentence mean exactly?

Can the same people sit across from each other more than once? For example, 1 sits in the first seat, and going clockwise, 2 is next all the way to five. Let's say in this case 3 sits across from 1. Can we change the order of 2, 4, and 5, and keep 1 and 3 the same? If 1 and 3 are across from each other, 2, 4, and 5, make 6 different combinations. Is this possible or does it mean they can't sit next to each other?
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Re: Statistics - Gmatprep [#permalink]  30 Oct 2009, 20:14
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lagomez wrote:
ralucaroman wrote:

Two seating arrangements are considered different only when the positions of the people are different relative to each other.

What does this sentence mean exactly?

Can the same people sit across from each other more than once? For example, 1 sits in the first seat, and going clockwise, 2 is next all the way to five. Let's say in this case 3 sits across from 1. Can we change the order of 2, 4, and 5, and keep 1 and 3 the same? If 1 and 3 are across from each other, 2, 4, and 5, make 6 different combinations. Is this possible or does it mean they can't sit next to each other?

xy and yx are same but xy, xz, and yz are different...
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Re: Statistics - Gmatprep [#permalink]  31 Oct 2009, 07:26
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GMAT TIGER wrote:
lagomez wrote:
ralucaroman wrote:

Two seating arrangements are considered different only when the positions of the people are different relative to each other.

What does this sentence mean exactly?

Can the same people sit across from each other more than once? For example, 1 sits in the first seat, and going clockwise, 2 is next all the way to five. Let's say in this case 3 sits across from 1. Can we change the order of 2, 4, and 5, and keep 1 and 3 the same? If 1 and 3 are across from each other, 2, 4, and 5, make 6 different combinations. Is this possible or does it mean they can't sit next to each other?

xy and yx are same but xy, xz, and yz are different...

So it has to do with the person sitting next to you and not across. Why was I thinking across? I think I've seen a question like this and it was across..but I could be wrong.

Thanks for the clarification
Re: Statistics - Gmatprep   [#permalink] 31 Oct 2009, 07:26
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