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Updated on: 08 Dec 2014, 05:26
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.
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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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
71% (00:24) correct
29%
(00:46)
wrong
based on 713
sessions
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Time
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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
A. 16
B. 48
C. 96
D. 120
E. 720
08 Dec 2014, 05:31
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portfolio1
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
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
P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 3 and 7! Thank you.
26 Dec 2015, 21:36
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Anonamy
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
