Arrangements at a round table question

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houstonrockets16: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Mon Feb 02, 2009 4:45 pm; Thanked: 1 times

by houstonrockets16 » Mon Aug 16, 2010 11:15 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 seatnig arrangements for the group?

a) 5 b) 10 c) 24 d) 32 e) 120

Please help! =) I am really struggling to come up with this answer..
thank you guys

CORRECT ANSWER: [spoiler]C) 24[/spoiler]

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Source: Beat The GMAT — Problem Solving | Mon Aug 16, 2010 11:15 am

Prashantbhardwaj: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Wed Aug 11, 2010 8:47 pm; Thanked: 3 times

by Prashantbhardwaj » Mon Aug 16, 2010 11:20 am

Its a simple circular permutation question.

where total no of permutations is = nPr/r

5P5 / 5 = 5! / 5 = 24 Ans.

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Gurpinder: Legendary Member; Posts: 659; Joined: Mon Dec 14, 2009 8:12 amFollowed by: 3 members; Thanked: 32 times

by Gurpinder » Mon Aug 16, 2010 11:24 am

houstonrockets16 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 seatnig arrangements for the group?

a) 5 b) 10 c) 24 d) 32 e) 120

Please help! =) I am really struggling to come up with this answer..
thank you guys

CORRECT ANSWER: [spoiler]C) 24[/spoiler]

Anytime you have a circular permutation problem remember this: (the total # - 1 ) factorial

So the total number of people here is 5. Therefore (5-1)! = 24.

"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.

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madhukumar_v: Senior | Next Rank: 100 Posts; Posts: 75; Joined: Thu Oct 23, 2008 4:25 am; Thanked: 6 times; GMAT Score:620

by madhukumar_v » Mon Aug 16, 2010 11:53 am

Two formulae for circular permutation.

1. (n-1)!

2. (n-1)!/2 (If you want to consider people sitting on the opposite ends when flipped to be the same)
Example: for 4 people, 1-2-3-4

1 1
3 2 = 2 3
4 4

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srajan: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Fri Jun 08, 2007 3:29 pm

by srajan » Mon Aug 16, 2010 4:37 pm

I would like to point out that if you had another condition that the chair is also important then the answer was 120.

Consider that there are 5 chairs and seating on a different chair makes a different arrangement then you would have 5P5.
i.e. 5! = 120
But since nothing sort of that is mentioned 5P5/5=24 is the correct answer.

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