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How many ways can six friends be arranged around a circular dinner tab

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How many ways can six friends be arranged around a circular dinner tab  [#permalink]

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New post Updated on: 08 Dec 2014, 05:26
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E

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How many ways can six friends be arranged around a circular dinner table?

A. 16
B. 48
C. 96
D. 120
E. 720

Originally posted by portfolio1 on 08 Dec 2014, 05:24.
Last edited by Bunuel on 08 Dec 2014, 05:26, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: How many ways can six friends be arranged around a circular dinner tab  [#permalink]

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New post 08 Dec 2014, 05:31
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portfolio1 wrote:
How many ways can six friends be arranged around a circular dinner table?

A. 16
B. 48
C. 96
D. 120
E. 720


The number of arrangements of n distinct objects in a row is given by \(n!\).
The number of arrangements of n distinct objects in a circle is given by \((n-1)!\).

The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have:

\(\frac{n!}{n} = (n-1)!\).

So, the answer is (6 - 1)! = 5! = 120.

Answer: D.

Check other SEATING ARRANGEMENTS IN A ROW AND AROUND A TABLE questions to practice.

Theory on Combinations: math-combinatorics-87345.html

DS questions on Combinations: search.php?search_id=tag&tag_id=31
PS questions on Combinations: search.php?search_id=tag&tag_id=52

Tough and tricky questions on Combinations: hardest-area-questions-probability-and-combinations-101361.html


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Re: How many ways can six friends be arranged around a circular dinner tab  [#permalink]

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New post 26 Dec 2015, 21:25
How do we arrive at 6!/6? I had chosen the answer for 6! only. What is the logic behind this please?
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Re: How many ways can six friends be arranged around a circular dinner tab  [#permalink]

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New post 26 Dec 2015, 21:36
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Anonamy wrote:
How do we arrive at 6!/6? I had chosen the answer for 6! only. What is the logic behind this please?



Hi,
in a normal row, say abcdef is the number of chair and mr x is one of the person sitting on these chairs...
in normal scenario/row , the moment x sits on a different chair a,b,c,d,e, or f, it is a new arrangement...
but it is different in case of a circle.. the seating arrangement is continous, there is no edge..
so say 1,2,3,4,5,6 are sitting on a,b,c,d,e,f respectively...
when they shift a sit to the right, the sitting arrangement becomes 6,1,2,3,4,5, which is different from 1,2,3,4,5,6( total 6 such arrangements)...
but in a circle 1,2,3,4,5,6 is same as 6,1,2,3,4,5 is same as 5,6,1,2,3,4.. because you are getting the same arrangement of people even if they have changed their seat because the relative positions have not changed.. that is why we divide by 6
Hope , the logic is clear
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Re: How many ways can six friends be arranged around a circular dinner tab  [#permalink]

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New post 05 Jun 2016, 14:11
ways in which 6 friends can sit around a circular table = (6-1)! = 5! = 120
Correct Answer - D
I wouldn't explain the logic again chetan has done it already very well
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How many ways can six friends be arranged around a circular dinner tab  [#permalink]

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New post 24 Jul 2017, 18:47
portfolio1 wrote:
How many ways can six friends be arranged around a circular dinner table?

A. 16
B. 48
C. 96
D. 120
E. 720


Formula to arrange \(n\) distinct objects in circle \(= (n−1)!\)

Number of ways 6 friends can be arranged around a circular dinner table \(= (6 -1)! = 5!\)

\(5! = 5*4*3*2*1 = 120\)

Answer (D)...
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Re: How many ways can six friends be arranged around a circular dinner tab  [#permalink]

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New post 26 Jul 2017, 16:10
portfolio1 wrote:
How many ways can six friends be arranged around a circular dinner table?

A. 16
B. 48
C. 96
D. 120
E. 720


Since we are seating 6 people around a circle, the people can be arranged in (6-1)! = 5! = 120 ways.

Answer: D
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Re: How many ways can six friends be arranged around a circular dinner tab  [#permalink]

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New post 02 Sep 2017, 13:11
portfolio1 wrote:
How many ways can six friends be arranged around a circular dinner table?

A. 16
B. 48
C. 96
D. 120
E. 720


For a circle the formula departs from the traditional method so instead of 6! the formula is 5! (n-1!)

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Re: How many ways can six friends be arranged around a circular dinner tab  [#permalink]

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New post 02 Nov 2018, 08:57
portfolio1 wrote:
How many ways can six friends be arranged around a circular dinner table?

A. 16
B. 48
C. 96
D. 120
E. 720


OA:D

Number of ways six friends can be arranged around a circular dinner table \(=\frac{n!}{n}=\frac{6!}{6}=5!=120\)
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Re: How many ways can six friends be arranged around a circular dinner tab  [#permalink]

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New post 02 Nov 2018, 09:16
portfolio1 wrote:
How many ways can six friends be arranged around a circular dinner table?

A. 16
B. 48
C. 96
D. 120
E. 720


for any circular combination formulation is always : (n-1)!
so here n = 6
5! = 120
there are 120 ways in which 6 friends can be arranged around a circular table :)
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Re: How many ways can six friends be arranged around a circular dinner tab  [#permalink]

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New post 21 Mar 2019, 06:43
chetan2u wrote:
Anonamy wrote:
How do we arrive at 6!/6? I had chosen the answer for 6! only. What is the logic behind this please?



Hi,
in a normal row, say abcdef is the number of chair and mr x is one of the person sitting on these chairs...
in normal scenario/row , the moment x sits on a different chair a,b,c,d,e, or f, it is a new arrangement...
but it is different in case of a circle.. the seating arrangement is continous, there is no edge..
so say 1,2,3,4,5,6 are sitting on a,b,c,d,e,f respectively...
when they shift a sit to the right, the sitting arrangement becomes 6,1,2,3,4,5, which is different from 1,2,3,4,5,6( total 6 such arrangements)...
but in a circle 1,2,3,4,5,6 is same as 6,1,2,3,4,5 is same as 5,6,1,2,3,4.. because you are getting the same arrangement of people even if they have changed their seat because the relative positions have not changed.. that is why we divide by 6
Hope , the logic is clear


Thank you for explaining the logic behind 6!/6.

I am not the type of person who can just "memorize" a formula without understanding the logic behind it.

Hope the GMATClub community can benefit from my takeaway.

I got the wrong answer today, because I used the 6! formula which turns out to be the wrong logic as per your explanation.
Should similar question appears on the exam, I must get this type of question right.
Action item for exam: in a time-pressured situation, BE VERY CLEAR what the question is asking you for. Does it make sense for 6! ? Are you sure you are not double-counting any arrangement ? Draw it out (especially when you are not sure about which formula to use).
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Re: How many ways can six friends be arranged around a circular dinner tab   [#permalink] 21 Mar 2019, 06:43
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