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.
At a dinner party, 5 people are to be seated around a...
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 415
- Joined: Thu Oct 15, 2009 11:52 am
- Thanked: 27 times
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 :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.
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
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7243
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
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.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
Answer: C
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews