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GMAT PREP PS question

by alex.gellatly » Mon Apr 16, 2012 12:21 am
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

Thanks in advanced
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by killer1387 » Mon Apr 16, 2012 12:36 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

Thanks in advanced
Fix one guy,
rest can be arranged in 4! ways
hence answer is 4!= 24

hence C
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by Anurag@Gurome » Mon Apr 16, 2012 2:50 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

Thanks in advanced
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

The correct answer is C.
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by niketdoshi123 » Mon Apr 16, 2012 2:59 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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by GMATGuruNY » Mon Apr 16, 2012 3:01 am
I discussed how to count circular permutations here:

https://www.beatthegmat.com/seating-arra ... 85488.html
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