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# m01-q24

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Manager
Joined: 05 Jan 2009
Posts: 81

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16 May 2009, 07:39
I could not understand the OE. Can anybody please explain in detail

If 5 noble knights are to be seated at a round table, then how many different ways can they be seated?

(C) 2008 GMAT Club - m01#24

120
96
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35
24
Founder
Joined: 04 Dec 2002
Posts: 15138
Location: United States (WA)
GMAT 1: 750 Q49 V42

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25 May 2009, 00:05
To find the total number of Permutations for 5 knights (order matters) is 5!
However, since we have a round table and therefore a circle, then we are losing one spot and have only 4 unique combinations, so the answer is 4!

Here is a reference for C&P:
http://betterexplained.com/articles/eas ... binations/

Permutations and Combinations
Some theory and concepts
formulae-for-3-overlapping-sets-69014.html
permutations-combinations-help-is-on-the-way-10838.html
permutation-combination-and-probabilities-14706.html
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Manager
Joined: 01 Aug 2008
Posts: 117

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25 May 2009, 11:34
for circular arrangement always consider a reference point i.e. in the above question consider one knight as the reference point and arrange the rest of the knights w.r.t to the reference knight.

so, out of 5 knight if i take one knight as reference then i have 4 knights which i can arrange in 4! ways w.r.t the reference knight and therefore 4! is the number of possible ways.
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Intern
Joined: 30 May 2009
Posts: 14

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30 May 2009, 21:50
I read it years ago and still remember it..

for circular arrangement of n items = (n-1)!

the answer of this question is 4! = 24
Manager
Joined: 13 Mar 2009
Posts: 190

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07 Sep 2009, 05:39
Also Google 'circular permutations' for very good articles regarding this topic.
Senior Manager
Joined: 18 Aug 2009
Posts: 320

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07 Sep 2009, 08:05
cool... Thanks a lot.
Intern
Joined: 29 Jan 2011
Posts: 7

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03 Apr 2011, 19:54
Combinations and permutations are one of my weaknesses. I got this question wrong but I think I did the math correctly and I just interpreted the problem differently. At a circular table, there are (N-1)! relative positions (i.e. one knight relative to another) but there are N! combinations if one thinks of absolute positions at a circular table (i.e. if one knight is sitting in the northernmost seat, one in the easternmost seat, etc) correct? I considered absolute positions to be different even if relative positions were the same so I answered 5! or 120.

Two questions:
(1) Is my thinking regarding absolute and relative positions correct?
(2) Whenever we see a circular table question on the GMAT should we assume they're only asking about relative position?
Manager
Joined: 15 Mar 2011
Posts: 92

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21 Jun 2011, 17:20
Hi all,

The key to understand circular permutation (n objects/persons) is that we have to consider 1 object/person as fixed, then the problem become a normal permutation with n-1 objects/persons.
Intern
Joined: 16 Jun 2011
Posts: 32

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21 Jun 2011, 17:35
Now let's up an (n-1)! circular questions shows up on our gmat! It's good for padding time!
Intern
Joined: 04 Aug 2011
Posts: 43
Location: United States
GMAT 1: 570 Q45 V25
GPA: 4
WE: Information Technology (Computer Software)

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14 Jan 2012, 22:49
Simple question - In cicular permutataion n arrangement to be made - N-1 ! So answer E - 24
Re: m01-q24   [#permalink] 14 Jan 2012, 22:49
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# m01-q24

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