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## GMAT PREP PS question

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alex.gellatly GMAT Destroyer!
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GMAT PREP PS question Mon Apr 16, 2012 1:21 am
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• Lap #[LAPCOUNT] ([LAPTIME])
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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killer1387 GMAT Destroyer!
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Mon Apr 16, 2012 1:36 am
alex.gellatly wrote:
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

Fix one guy,
rest can be arranged in 4! ways

hence C

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Anurag@Gurome GMAT Instructor
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Mon Apr 16, 2012 3:50 am
alex.gellatly wrote:
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

For circular seating arrangement, the number of arrangements of n distinct objects in a row is given by n!.
Number of arrangements of n distinct objects in a circle is given by (n - 1)!.

So, in this the total number of different possible seating arrangements for the group = (5 - 1)! = 4! = 4 * 3 * 2 * 1 = 24 ways

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niketdoshi123 Really wants to Beat The GMAT!
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Mon Apr 16, 2012 3:59 am
the answer should be (n-1)! where,
n= total no. of people.
This is only valid if people are to be seated around a circular table (all the seats are considered to be identical).
so fix one guy's position and arrange others wrt him.
hence in this case the ans is (n-1)!= (5-1)! = 24 option C

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GMATGuruNY GMAT Instructor
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Mon Apr 16, 2012 4:01 am
I discussed how to count circular permutations here:

http://www.beatthegmat.com/seating-arrangement-t85488.html

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