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

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by AAPL » Wed Sep 26, 2018 6:24 am

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At a dinner party, 5 people are 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

OA C.
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At a dinner party, 5 people are seated around a circular tab

by fskilnik@GMATH » Wed Sep 26, 2018 8:24 am
AAPL wrote:GMAT Prep

At a dinner party, 5 people are 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
\[?\,\,\, = \,\,\,PC\left( 5 \right)\,\,\,\,\,\,\,\left[ {{\text{circular}}\,\,{\text{permutations}}\,\,{\text{of}}\,\,{\text{5}}\,\,{\text{distinct}}\,\,{\text{objects}}} \right]\]
\[? = \frac{{5!}}{5} = \left( {5 - 1} \right)! = 24\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Last edited by fskilnik@GMATH on Thu Sep 27, 2018 3:34 pm, edited 1 time in total.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by [email protected] » Wed Sep 26, 2018 8:47 am
Hi All,

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 unique arrangement of people could be created with 5 different 'starting chairs.' 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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by Scott@TargetTestPrep » Sat Sep 29, 2018 5:03 pm
AAPL wrote:GMAT Prep

At a dinner party, 5 people are 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 of ways 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

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