At a dinner party

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

At a dinner party

by sanju09 » Mon Mar 12, 2012 2:25 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

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Source: Beat The GMAT — Problem Solving | Mon Mar 12, 2012 2:25 am

killer1387: Legendary Member; Posts: 581; Joined: Sun Apr 03, 2011 7:53 am; Thanked: 52 times; Followed by:5 members

by killer1387 » Mon Mar 12, 2012 2:40 am

4! i.e. 24
Hence C

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Mon Mar 12, 2012 6:11 am

sanju09 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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