Aug 25 09:00 AM PDT  12:00 PM PDT Join a FREE 1day verbal workshop and learn how to ace the Verbal section with the best tips and strategies. Limited for the first 99 registrants. Register today! Aug 25 08:00 PM PDT  11:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE. Aug 28 08:00 AM PDT  09:00 AM PDT Join a FREE live webinar with examPAL and Admissionado and learn how to master GMAT Critical Reasoning questions and the 6pointed star of MBA application essay glory. Save your spot today! Aug 30 08:00 PM PDT  11:00 PM PDT We'll be posting questions in DS/PS/SC/CR in competition mode. Detailed and quickest solution will get kudos. Will be collecting new links to all questions in this topic. Here you can also check links to fresh questions posted. Aug 31 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes. Sep 01 07:00 AM PDT  09:00 AM PDT Want to solve 700+ level Algebra questions within 2 minutes? Attend this free webinar to learn how to master the most challenging Inequalities and Absolute Values questions in GMAT Sep 02 08:00 PM PDT  11:00 PM PDT Sign Up, Get $49 Exam Pack 2 FREE. Train to be ready for Round 1 Deadlines with EMPOWERgmat's Score Booster Code: EP22019 Ends: September 2nd
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 30 Aug 2006
Posts: 337

In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
15 Oct 2006, 09:32
Question Stats:
40% (02:04) correct 60% (02:05) wrong based on 383 sessions
HideShow timer Statistics
In how many ways can 6 people be seated at a round table if one of those seated cannot sit next to 2 of the other 5? a) 720 b) 120 c) 108 d) 84 e) 48
Official Answer and Stats are available only to registered users. Register/ Login.




Manager
Joined: 05 Oct 2006
Posts: 241

Re: In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
16 Oct 2006, 00:31
n people can be seated around a round table in (n1)! ways.
ok...let's find the no of ways in which that person is always seated next to 2 particular people.these 3 can be seated in 2 ways because the cetre position is fixed.
now we have a total of 3+1 people...note that 1 represents the group of those 3 people.
so 4 can be seated in (41)! ways = 6 ways.
hence total ways when 2 particular people are always next to one particular of them = 2*6=12 ways..
and total no of ways in which 6 people can be seated =(61)!=120 ways..
hence answer= 120=12 = 108 ways.
choice b as per me.
what's the OA?
londonluddite wrote: In how many ways can 6 people be seated at a round table if one of those seated cannot sit next to 2 of the other 5?
a) 720 b) 120 c) 108 d) 84 e) 48




Senior Manager
Joined: 08 Jun 2006
Posts: 295
Location: Washington DC

Re: In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
15 Oct 2006, 11:12
6 People in a round table can be seated in (6  1) ! ways = 120.
Now we need to subtract the number of cases when one of those is sitting next to 2 of the other 5.
We can consider as if 5 people are sitting in a row because it is round table.
Again consider 3 people, those who can not sit together, as a single unit â€“
So the possible arrangements among remaining people 5 â€“ 3 + 1 Unit are = 3 !
And the 3 people unit can arrange among themselves in 3 ! ways.
So the possible cases when one of those is sitting next to 2 of the other 5 = 3 ! * 3 ! = 36
Total possible cases = 120 36 = 84



Manager
Joined: 08 Jul 2006
Posts: 84

Re: In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
15 Oct 2006, 12:10
Can someone tell me where I go wrong reasoning it this way.
Say the six people are A B C D E F and A cannot sit next to E and F
There would be 6 ways to sit A, 3 ways to sit the second person (on A's rightside), 2 ways to sit the third person (on A's leftside), 3 ways to sit the fourth, 2 ways to sit the fifth, and 1 way to sit the sixth.
6x3x3x2x2x1 = 216
I get 216. Where am I going wrong using this approach????



Manager
Joined: 13 Sep 2006
Posts: 197

Re: In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
15 Oct 2006, 14:46
anindyat wrote: 6 People in a round table can be seated in (6  1) ! ways = 120.
Now we need to subtract the number of cases when one of those is sitting next to 2 of the other 5.
We can consider as if 5 people are sitting in a row because it is round table. Again consider 3 people, those who can not sit together, as a single unit â€“
So the possible arrangements among remaining people 5 â€“ 3 + 1 Unit are = 3 ! And the 3 people unit can arrange among themselves in 3 ! ways.
So the possible cases when one of those is sitting next to 2 of the other 5 = 3 ! * 3 ! = 36
Total possible cases = 120 36 = 84
I understand that we need the total number of ways minus the exceptions...
but could someone explain why seating 6 people is not 6*5*4*3*2*1 = 720?
Why is it (61)!



Director
Joined: 25 Jun 2006
Posts: 986

Re: In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
15 Oct 2006, 22:09
I dont get the question.
how can 1 one of them not sit next to the other 2 in a round table?



Senior Manager
Joined: 30 Aug 2006
Posts: 337

Re: In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
16 Oct 2006, 11:19
OA is C.
OE: 6 people can be seated round around a table in 5! ways (would appreciate someones clarification on whether this is correct and why). There are 2 ways the two unwelcome guests could sit next to the person in question and 3! ways of arranging the other three. This is subtracted from 5! giving a result of 108.
Clear as mud
Edit : AK why can n people be seated in (n1)! ways and not n!
Thanks



Retired Moderator
Joined: 05 Jul 2006
Posts: 1627

Re: In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
16 Oct 2006, 11:24
London .... if you allow me to answer ur question.....
it is because we have to reserve one place (the one in n1)
as a refrence from which we start arranging and counting (because in a round shape we have no end and start points
Hope this Helps



Math Expert
Joined: 02 Sep 2009
Posts: 57272

Re: In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
19 Nov 2014, 04:46
londonluddite wrote: In how many ways can 6 people be seated at a round table if one of those seated cannot sit next to 2 of the other 5?
a) 720 b) 120 c) 108 d) 84 e) 48 Check other Seating Arrangements in a Row and around a Table Questions.
_________________



Intern
Joined: 23 Dec 2014
Posts: 8

Re: In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
21 Jan 2015, 03:39
I may not able to get the question properly. Let me put forward my thought process:
Required no. of ways = Total no. of ways  when one of them is sitting next to 2 of other 5.
Now this question statement i.e. "one of those seated cannot sit next to 2 of the other 5" seems tricky to me. Let me split in parts:
1. "One of those.." Who out of 6 ?? There can be 6 ways to choose one out of 6.
2. "2 of the other 5"..Who 2 out of 5?? There can be 10 ways to choose 2 out of 5.
3. "when one of them is sitting next to 2 of other"  Suppose B is one out of 6 and A & C are 2 out of 5. Then does statement means that B should be in mid of A and C?
I was little confused here. But then i understand yes it should mean B is in mid of A & C. Any comments here most welcome..
So now lets find the actual no of ways for each type:
No. of ways When AB are together = Now we are left with 4 + 1(AB) = 5 people. SO no of circular ways = (51)! = 4! * 2!( A and B can be arranged themselves)
Now bind ABC together we are left with 3 + 1(ABC) = 4 people. No. of ways it can be arranged is (41)! * 2!(as A and C can be interchanged) = 12 ways
Total no. of ways = (61)! = 5! So required no of ways = 5! 3!*2! = 120  12 = 108. Now shall we not consider the above point 1 and 2? if yes, then we should multiply by 6 and 10, isn't??
So total ways = 6*10*108 ??
Let me tweak the question little bit(as this was the reason of my initial confusion). What if instead of "one of those seated cannot sit next to 2 of the other 5"
question says "one of those seated cannot sit next any 2 of the other 5". Then to find this i had below analysis.
Then to find out no of ways "when one of them is sitting next to any 2 of other" = No. of ways When AB are together + No of ways when BC are together  No . of ways
when ABC are together and position of A, B and C is fixed in that arrangement i.e. A,B,C are binded together but should not be arraneged themselves.
The reason we are subtracting "No . of ways when ABC are together and position of A, B and C is fixed in that arrangement." is we have counted this twice when we have summed up "No. of ways When AB are together" and "No of
ways when BC are together".
For example: No. of ways When AB are together  Includes.... ABC and No. of ways When BC are together also includes... ABC Given position of A, B and C is fixed.
So No. of ways When AB are together means 4 + 1 (AB) = 5 people to be arranged in circular way. So it should be (51)! * 2(A and B can be interchanged) = 48 ways.
Likewise, No of ways when BC are together = 48.
No . of ways when ABC are together but arranged themselves = 3 + 1 (A,B,C) = (41)! = 6 ways
The no of ways "when one of them is sitting next to any 2 of other 5" = 48 + 48  6 = 90.
Required no. of ways = Total no. of ways  when one of them is sitting next to any 2 of other 5. Required no. of ways = 120  90 = 30 ways.
Now again considering point 1 and 2 = 6*10*30 = 1800 isn't?
I would request Experts/Bunuel to comment here.
Thanks Manoj Parashar



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2967
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
04 Jul 2015, 10:01
Quote: In how many ways can 6 people A,B,C,D,E,F be seated at a round table if B cannot sit next to A and/or C?
a) 720 b) 120 c) 108 d) 84 e) 36 Have Modified the Language to make it clearer6 people are A, B, C, D, E and F and B can not sit next to A and C Considering the Position of B is fixed, We have to make sure that 2 person who sit next to B are out of D, E and F i.e. No. of ways of choosing the neighbours of B = 3 C2 = 3 and the no. of ways the Selected neighbours can arrange at the two position adjacent to B = 2! i.e. The ways the B and The neighbours can be arranged = 3 C2 *2! = 3*2 = 6 Now The no. of ways in which Remaining Three Individuals can be arranged on remaining 3 seats = 3! Total Ways of making Six person seated such that B doesn't sit next to A and C = 3 C2 *2!*3! = 36
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Manager
Joined: 13 Oct 2013
Posts: 135
Concentration: Strategy, Entrepreneurship

In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
04 Jul 2015, 10:26
Hi, Can i solve this by taking total number of arrangements i.e 5!=120 ways and then subtract the restriction? 120(arrangements B should not sit next to A and/or C) ? is that a correct approach? GMATinsight wrote: Quote: In how many ways can 6 people A,B,C,D,E,F be seated at a round table if B cannot sit next to A and/or C?
a) 720 b) 120 c) 108 d) 84 e) 36 Have Modified the Language to make it clearer6 people are A, B, C, D, E and F and B can not sit next to A and C Considering the Position of B is fixed, We have to make sure that 2 person who sit next to B are out of D, E and F i.e. No. of ways of choosing the neighbours of B = 3 C2 = 3 and the no. of ways the Selected neighbours can arrange at the two position adjacent to B = 2! i.e. The ways the B and The neighbours can be arranged = 3 C2 *2! = 3*2 = 6 Now The no. of ways in which Remaining Three Individuals can be arranged on remaining 3 seats = 3! Total Ways of making Six person seated such that B doesn't sit next to A and C = 3 C2 *2!*3! = 36
_________________
 Kindly press +1 Kudos if my post helped you in any way



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2967
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
04 Jul 2015, 11:13
sunita123 wrote: Hi, Can i solve this by taking total number of arrangements i.e 5!=120 ways and then subtract the restriction? 120(arrangements B should not sit next to A and/or C) ? is that a correct approach? GMATinsight wrote: Quote: In how many ways can 6 people A,B,C,D,E,F be seated at a round table if B cannot sit next to A and/or C?
a) 720 b) 120 c) 108 d) 84 e) 36 Have Modified the Language to make it clearer6 people are A, B, C, D, E and F and B can not sit next to A and C Considering the Position of B is fixed, We have to make sure that 2 person who sit next to B are out of D, E and F i.e. No. of ways of choosing the neighbours of B = 3 C2 = 3 and the no. of ways the Selected neighbours can arrange at the two position adjacent to B = 2! i.e. The ways the B and The neighbours can be arranged = 3 C2 *2! = 3*2 = 6 Now The no. of ways in which Remaining Three Individuals can be arranged on remaining 3 seats = 3! Total Ways of making Six person seated such that B doesn't sit next to A and C = 3 C2 *2!*3! = 36 That would be fine but a difficult approach as you will have to calculate three casesCase1: When A sits next to B and C does not sit next to B A can sit next to B in 2 ways (On B's right or B's left side) The next adjacent place of B can be occupied in 3 ways because C can't sit next to B Remaining three can sit in 3! ways So total ways = 2*3*3! = 36 ways Case2: When C sits next to B and A does not sit next to B C can sit next to B in 2 ways (On B's right or B's left side) The next adjacent place of B can be occupied in 3 ways because A can't sit next to B Remaining three can sit in 3! ways So total ways = 2*3*3! = 36 ways Case3: When A and C both sit on either sides of B A and C can sit in 2! ways on two places adjacent to B Remaining three can sit in 3! ways So total ways = 2!*3! = 12 ways Total Unfavourable cases = 36+36+12 = 84 ways Total favourable Cases = (61)!  84 = 120  84 = 36 ways I hope it helps!
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Intern
Joined: 21 Jun 2014
Posts: 28

Re: In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
04 Jul 2015, 11:52
6 People Sitting Around a Round Table Without Any Restriction = (61)! = 5! = 120
Restriction = 1 person cannot sit around other two particular people Complement Condition = 3 People Will Always Sit together Now considering 3 People as one group along with other 3 people , total number of ways they can sit = (41) = 3! = 6 Ways But group of 3 Can also Adjust it self in 3! ways = 6 Ways Total Complement Ways = 6+6 = 12
Total Ways = 120  12 = 108
Please correct, if this is not the right way of solving the question



Current Student
Joined: 03 Aug 2011
Posts: 279
Concentration: Strategy, Finance
GMAT 1: 640 Q44 V34 GMAT 2: 700 Q42 V44 GMAT 3: 680 Q44 V39 GMAT 4: 740 Q49 V41
GPA: 3.7
WE: Project Management (Energy and Utilities)

Re: In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
20 Aug 2015, 04:48
I knew the (n1)! formula which doesn't solve the entire problem here so I shifted gears and came to the following approach. You have 6 spots on the table. Let's imagine to fix the guy who can't sit with all the other ones on one of the spots. (1) As he can't stand 2 out of total of 5 people, we have 3 options for the 2 seats next to him  so 3C2 which equals 3. (2) For the remaining 3 spots we have 3! or 6 options. Multiply (1) and (2) and you get 18 seating arrangements. But bear with me, we have to remember that we fixed the bad guy on just one spot. He can sit on every seat on the table, namely  6. So multiply the 18 seating arrangements with 6 and you get 108 (C)
_________________
Thank you very much for reading this post till the end! Kudos?



Manager
Joined: 10 Jun 2015
Posts: 116

In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
20 Aug 2015, 05:40
londonluddite wrote: In how many ways can 6 people be seated at a round table if one of those seated cannot sit next to 2 of the other 5?
a) 720 b) 120 c) 108 d) 84 e) 48 I get a different answer. Let me explain how I worked out. I fixed the person say A, who cannot sit with 2 of the other 5, in one place. Now, the remaining 3 persons who can be seated to the next seats of A can be done in 3p2 ways (6 ways) Note that we don't need to select those 3 from 5 because when you keep the 2 away the remaining 3 can be seated with A. Now, the remaining 3 persons can be seated in the remaining 3 seats in 3p3 or 6 ways. Therefore, 6*6=36 ways.



Manager
Joined: 23 Sep 2015
Posts: 82
Concentration: General Management, Finance
GMAT 1: 680 Q46 V38 GMAT 2: 690 Q47 V38
GPA: 3.5

Re: In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
24 Oct 2015, 09:20
can someone provide a more clear answer for this?



CEO
Joined: 20 Mar 2014
Posts: 2619
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
24 Oct 2015, 10:13
GMATDemiGod wrote: can someone provide a more clear answer for this? It is explained clearly in the post inhowmanywayscan6peoplebeseatedataroundtableif36750.html#p253783Can you mention what exactly is the issue?



Manager
Joined: 23 Sep 2015
Posts: 82
Concentration: General Management, Finance
GMAT 1: 680 Q46 V38 GMAT 2: 690 Q47 V38
GPA: 3.5

In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
24 Oct 2015, 10:52
I was trying to do this by:
6 people ( A B C D E F)
Fix A
A cannot sit next to B or C
Case 1 B/C to the left of A
1*4!*2!
Case 2 B/C ro the right of A
1*4!*2!
Then took anyway the case when A and B is to the left and right to not double count
3!
I don't see why i cannot do it this way. Will check the link provided see if i can clear this up
__________
I think i misinterpreted it to mean, A or B, instead of A and B.



Intern
Joined: 27 May 2016
Posts: 2

In how many ways can 6 people be seated at a round table if
[#permalink]
Show Tags
21 Jun 2016, 19:19
So is the correct answer 36? The original post says 108.




In how many ways can 6 people be seated at a round table if
[#permalink]
21 Jun 2016, 19:19



Go to page
1 2
Next
[ 27 posts ]



