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

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

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

by BTGmoderatorLU » Fri Dec 01, 2017 1:49 pm

At a dinner party 5 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of possible sitting arrangements or the group?

A. 5
B. 10
C. 24
D. 32
E. 120

The OA is C.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Fri Dec 01, 2017 1:49 pm

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by [email protected] » Fri Dec 01, 2017 4:18 pm

Hi LUANDATO,

We're told that 5 people are to be seated around a circular table and that two sitting arrangements are considered different only when the positions of the people are different relative to each other. We're asked for the total number of possible sitting arrangements of the group.

If the 5 people were sitting in a straight-line, then we'd be dealing with a standard Permutation question - and there would be 5! = 120 possible arrangements. Here, we're dealing with a circular table, so any of the 5 chairs could be the "first chair" and 1 arrangement of people could be created in 5 different ways. Thus, we have to divide 120 by 5 to determine the number of unique arrangements. 120/5 = 24 arrangements.

Final Answer: C

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sat Dec 02, 2017 3:24 am

To count circular arrangements:
1. Place someone in the circle.
2. Count the number of ways to arrange the REMAINING people.

LUANDATO wrote:At a dinner party 5 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of possible sitting arrangements or the group?

A. 5
B. 10
C. 24
D. 32
E. 120

After one of the 5 people has been placed at the table, the number of ways to arrange the remaining 4 people = 4! = 24.

The correct answer is C.

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by Scott@TargetTestPrep » Thu Jan 11, 2018 2:14 pm

LUANDATO wrote:At a dinner party 5 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of possible sitting arrangements or 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 one 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

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