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by dreamv » Wed Feb 22, 2012 2:20 pm
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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by GMATGuruNY » Wed Feb 22, 2012 3:02 pm
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by Anurag@Gurome » Wed Feb 22, 2012 8:01 pm
dreamv 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

The correct answer is C.
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by pemdas » Wed Feb 22, 2012 11:17 pm
note the words underlined in quote below and apply combination/permutation concepts
(5-1)!=24
c
dreamv wrote:At a dinner party, 5 people are to be seated around a circular table (circular arrangement, (n-1)! ). Two seating arrangements are considered different only when the positions of the people are different relative to each other (objects are distinct, hence use permutation or ordered arrangement). 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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