At a dinner party, 5 people are to be seated around a...

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Tue Feb 27, 2018 8:01 am

At a dinners party, 5 people are seated around a circular table. 2 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

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

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Source: Beat The GMAT — Problem Solving | Tue Feb 27, 2018 8:01 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Tue Feb 27, 2018 9:53 am

swerve wrote:At a dinners party, 5 people are seated around a circular table. 2 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

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

You can start by calculating the number of permutations of 5 people. For example, pick a chair to begin with. There are 5 ways to fill that chair. Continue clockwise with the remaining people, so :

5x4x3x2x1 = 120 arrangements

However, visualize that contributing to the total number of arrangements are arrangements where the same relative positioning of the five people is maintained but that each person is shifted one chair clockwise. Since question asks for those arrangements where only the relative positions are different, you need to divide 120 by 5 = 24,C

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Mar 01, 2018 5:43 pm

swerve wrote:At a dinners party, 5 people are seated around a circular table. 2 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

When determining the number way to arrange a group around a circle, we subtract 1 from the total and set it to a factorial. Thus, the total number of possible sitting arrangements for 5 people around a circular table is 4! = 24.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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