Jun 18 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, June 18th at 9 pm ET Jun 18 10:00 PM PDT  11:00 PM PDT Send along your receipt from another course or book to info@empowergmat.com and EMPOWERgmat will give you 50% off the first month of access OR $50 off the 3 Month Plan Only available to new students Ends: June 18th Jun 19 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Jun 22 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jun 23 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 24 Nov 2014
Posts: 3

How many ways can six friends be arranged around a circular dinner tab
[#permalink]
Show Tags
Updated on: 08 Dec 2014, 05:26
Question Stats:
66% (00:27) correct 34% (00:48) wrong based on 182 sessions
HideShow timer Statistics
How many ways can six friends be arranged around a circular dinner table? A. 16 B. 48 C. 96 D. 120 E. 720
Official Answer and Stats are available only to registered users. Register/ Login.
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.




Math Expert
Joined: 02 Sep 2009
Posts: 55631

Re: How many ways can six friends be arranged around a circular dinner tab
[#permalink]
Show Tags
08 Dec 2014, 05:31
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 \((n1)!\). 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: \(\frac{n!}{n} = (n1)!\). So, the answer is (6  1)! = 5! = 120. Answer: D. Check other SEATING ARRANGEMENTS IN A ROW AND AROUND A TABLE questions to practice. P.S. Please read carefully and follow: rulesforpostingpleasereadthisbeforeposting133935.html Pay attention to rules 3 and 7! Thank you.
_________________




Manager
Joined: 01 Aug 2014
Posts: 54

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



Math Expert
Joined: 02 Aug 2009
Posts: 7752

Re: How many ways can six friends be arranged around a circular dinner tab
[#permalink]
Show Tags
26 Dec 2015, 21:36
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
_________________



Senior Manager
Joined: 24 Nov 2015
Posts: 496
Location: United States (LA)

Re: How many ways can six friends be arranged around a circular dinner tab
[#permalink]
Show Tags
05 Jun 2016, 14:11
ways in which 6 friends can sit around a circular table = (61)! = 5! = 120 Correct Answer  D I wouldn't explain the logic again chetan has done it already very well



Director
Joined: 04 Dec 2015
Posts: 740
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)

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



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6563
Location: United States (CA)

Re: How many ways can six friends be arranged around a circular dinner tab
[#permalink]
Show Tags
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 (61)! = 5! = 120 ways. Answer: D
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Director
Joined: 12 Nov 2016
Posts: 715
Location: United States
GPA: 2.66

Re: How many ways can six friends be arranged around a circular dinner tab
[#permalink]
Show Tags
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! (n1!) D



Senior Manager
Joined: 18 Jun 2018
Posts: 267

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



Intern
Joined: 09 Jul 2017
Posts: 27

Re: How many ways can six friends be arranged around a circular dinner tab
[#permalink]
Show Tags
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 : (n1)! so here n = 6 5! = 120 there are 120 ways in which 6 friends can be arranged around a circular table



Intern
Joined: 01 Feb 2019
Posts: 15

Re: How many ways can six friends be arranged around a circular dinner tab
[#permalink]
Show Tags
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 timepressured situation, BE VERY CLEAR what the question is asking you for. Does it make sense for 6! ? Are you sure you are not doublecounting any arrangement ? Draw it out (especially when you are not sure about which formula to use).




Re: How many ways can six friends be arranged around a circular dinner tab
[#permalink]
21 Mar 2019, 06:43






