Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 13 Feb 2016, 08:12

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# At a dinner party 5 people are to be seated around a circula

Author Message
TAGS:
Intern
Joined: 20 May 2012
Posts: 20
Followers: 0

Kudos [?]: 17 [2] , given: 9

At a dinner party 5 people are to be seated around a circula [#permalink]  23 Mar 2013, 20:36
2
KUDOS
4
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

69% (01:22) correct 31% (00:33) wrong based on 172 sessions
At a dinner party 5 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other.What is the total number of possible sitting arrangements or the group?

A. 5
B. 10
C. 24
D. 32
E. 120
[Reveal] Spoiler: OA
Manager
Joined: 27 Jan 2013
Posts: 199
GMAT 1: 780 Q49 V51
Followers: 40

Kudos [?]: 165 [1] , given: 20

Re: At a dinner party 5 people are to be seated around a circula [#permalink]  23 Mar 2013, 21:00
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
Hi there,

You can treat this as an ordering question except that for a circular arrangement you need to divide by the number of spaces. So in this case:

5!/5=24

If you spin the circle to right, that doesn't count as a new arrangement. Dividing by the number of spaces takes that into consideration.

Happy Studies,

HG.
_________________

"It is a curious property of research activity that after the problem has been solved the solution seems obvious. This is true not only for those who have not previously been acquainted with the problem, but also for those who have worked over it for years." -Dr. Edwin Land

GMAT vs GRE Comparison

If you found my post useful KUDOS are much appreciated.

Here is the first set along with some strategies for approaching this work: http://gmatclub.com/forum/the-economist-reading-comprehension-challenge-151479.html

Math Expert
Joined: 02 Sep 2009
Posts: 31304
Followers: 5364

Kudos [?]: 62542 [0], given: 9457

Re: At a dinner party 5 people are to be seated around a circula [#permalink]  24 Mar 2013, 01:21
Expert's post
5
This post was
BOOKMARKED
Val1986 wrote:
At a dinner party 5 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other.What is the total number of possible sitting arrangements or the group?

A. 5
B. 10
C. 24
D. 32
E. 120

We have a case of circular arrangement.

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 $$(n-1)!$$.

From Gmat Club Math Book (combinatorics chapter):
"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:

$$R = \frac{n!}{n} = (n-1)!$$"

$$(n-1)!=(5-1)!=24$$

seven-men-and-seven-women-have-to-sit-around-a-circular-92402.html
a-group-of-four-women-and-three-men-have-tickets-for-seven-a-88604.html
the-number-of-ways-in-which-5-men-and-6-women-can-be-seated-94915.html
4-couples-are-seating-at-a-round-tables-how-many-ways-can-131048.html
at-a-party-5-people-are-to-be-seated-around-a-circular-104101.html
seven-family-members-are-seated-around-their-circular-dinner-102184.html
seven-men-and-seven-women-have-to-sit-around-a-circular-11473.html
a-group-of-8-friends-sit-together-in-a-circle-alice-betty-106928.html
seven-men-and-five-women-have-to-sit-around-a-circular-table-98185.html
a-group-of-8-friends-sit-together-in-a-circle-alice-betty-106928.html
find-the-number-of-ways-in-which-four-men-two-women-and-a-106919.html
gmat-club-monday-giveaway-155157.html (700+)

Hope it helps.
_________________
Manager
Joined: 23 Jan 2013
Posts: 173
Concentration: Technology, Other
Schools: Haas
GMAT Date: 01-14-2015
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 33 [0], given: 41

Re: At a dinner party 5 people are to be seated around a circula [#permalink]  24 Mar 2013, 01:58
I am a little weak in combinatorics , could some one explain to be why the answer is not 5! .
Math Expert
Joined: 02 Sep 2009
Posts: 31304
Followers: 5364

Kudos [?]: 62542 [1] , given: 9457

Re: At a dinner party 5 people are to be seated around a circula [#permalink]  24 Mar 2013, 02:00
1
KUDOS
Expert's post
shelrod007 wrote:
I am a little weak in combinatorics , could some one explain to be why the answer is not 5! .

Check here: at-a-dinner-party-5-people-are-to-be-seated-around-a-circula-149709.html#p1201656

_________________
Intern
Joined: 20 May 2012
Posts: 20
Followers: 0

Kudos [?]: 17 [0], given: 9

Re: At a dinner party 5 people are to be seated around a circula [#permalink]  24 Mar 2013, 07:55
HerrGrau wrote:
Hi there,

You can treat this as an ordering question except that for a circular arrangement you need to divide by the number of spaces. So in this case:

5!/5=24

If you spin the circle to right, that doesn't count as a new arrangement. Dividing by the number of spaces takes that into consideration.

Happy Studies,

HG.

Thank you so much HG!

This was a very simple and concise explanation! SO if there were 10 people seated at the circular table, we would solve it as 10!/10?

Thanks once again!
Manager
Joined: 27 Jan 2013
Posts: 199
GMAT 1: 780 Q49 V51
Followers: 40

Kudos [?]: 165 [0], given: 20

Re: At a dinner party 5 people are to be seated around a circula [#permalink]  24 Mar 2013, 11:34
Expert's post
You are very welcome. Yes, 10!/10 is exactly right for 10 people around a circular table.

HG.
_________________

"It is a curious property of research activity that after the problem has been solved the solution seems obvious. This is true not only for those who have not previously been acquainted with the problem, but also for those who have worked over it for years." -Dr. Edwin Land

GMAT vs GRE Comparison

If you found my post useful KUDOS are much appreciated.

Here is the first set along with some strategies for approaching this work: http://gmatclub.com/forum/the-economist-reading-comprehension-challenge-151479.html

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6238
Location: Pune, India
Followers: 1683

Kudos [?]: 9656 [0], given: 198

Re: At a dinner party 5 people are to be seated around a circula [#permalink]  24 Mar 2013, 21:01
Expert's post
Val1986 wrote:
At a dinner party 5 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other.What is the total number of possible sitting arrangements or the group?

A. 5
B. 10
C. 24
D. 32
E. 120

Check out this post on circular arrangements. It discusses why the number of arrangements is n!/n (which is the same as (n-1)!) in case there are n people sitting around a round table.
http://www.veritasprep.com/blog/2011/10 ... angements/

It also discusses the relevance of this statement in the question: "Two sitting arrangements are considered different only when the positions of the people are different relative to each other"
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 07 Feb 2011 Posts: 88 Followers: 0 Kudos [?]: 44 [0], given: 43 Re: At a dinner party 5 people are to be seated around a circula [#permalink] 25 Mar 2013, 02:03 shelrod007 wrote: I am a little weak in combinatorics , could some one explain to be why the answer is not 5! . The short answer would be something like this to your question rephrased (why isn't it n! instead of n-1! ?) The reason is that RELATIVE to each other, ie (BAC) (CAB) ie BA AB CA AC, are seated next to each other and can be considered 'one group' _________________ We appreciate your kudos' Senior Manager Joined: 15 Aug 2013 Posts: 328 Followers: 0 Kudos [?]: 34 [0], given: 23 Re: At a dinner party 5 people are to be seated around a circula [#permalink] 23 Apr 2014, 18:41 VeritasPrepKarishma wrote: Val1986 wrote: At a dinner party 5 people are to be seated around a circular table. Two sitting arrangements are considered different only when the positions of the people are different relative to each other.What is the total number of possible sitting arrangements or the group? A. 5 B. 10 C. 24 D. 32 E. 120 Check out this post on circular arrangements. It discusses why the number of arrangements is n!/n (which is the same as (n-1)!) in case there are n people sitting around a round table. http://www.veritasprep.com/blog/2011/10 ... angements/ It also discusses the relevance of this statement in the question: "Two sitting arrangements are considered different only when the positions of the people are different relative to each other" Hi Karishma, If there were constraints such as A can't be next to B or C, does that mean that we now have 5 seats but since 3 of them are fixed, the solution would be 2!/2? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6238 Location: Pune, India Followers: 1683 Kudos [?]: 9656 [1] , given: 198 Re: At a dinner party 5 people are to be seated around a circula [#permalink] 23 Apr 2014, 19:18 1 This post received KUDOS Expert's post russ9 wrote: Hi Karishma, If there were constraints such as A can't be next to B or C, does that mean that we now have 5 seats but since 3 of them are fixed, the solution would be 2!/2? I am assuming your question is this: 5 people are to be seated around a circular table such that A sits neither next to B nor next to C. How many arrangements are possible? I don't know how you consider "...3 of them are fixed". The way you handle this constraint would be this: There are 5 vacant seats. Make A occupy 1 seat in 1 way (because all seats are same before anybody sits). Now we have 4 unique vacant seats (unique with respect to A) and 4 people. B and C cannot sit next to A so D and E occupy the seats right next to A on either side. This can be done in 2! ways: D A E or E A D B and C occupy the two unique seats away from A. This can be done in 2! ways. Total number of arrangements = 2! * 2! = 4 Check out these posts. First discusses theory of circular arrangements and next two discuss circular arrangements with various constraints: http://www.veritasprep.com/blog/2011/10 ... angements/ http://www.veritasprep.com/blog/2011/10 ... ts-part-i/ http://www.veritasprep.com/blog/2011/11 ... 3-part-ii/ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Intern
Joined: 19 May 2015
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 0

At a dinner party 5 ppl are to seated around a circular table [#permalink]  01 Sep 2015, 19:08
At a dinner party 5 ppl are to seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of possible seating arrangements for the people.

A.5
B.10
C.24
D.32
E.120
Math Expert
Joined: 02 Sep 2009
Posts: 31304
Followers: 5364

Kudos [?]: 62542 [0], given: 9457

Re: At a dinner party 5 people are to be seated around a circula [#permalink]  01 Sep 2015, 21:06
Expert's post
dotty2504 wrote:
At a dinner party 5 ppl are to seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of possible seating arrangements for the people.

A.5
B.10
C.24
D.32
E.120

Merging topics. Please refer to the discussion above.

_________________
Re: At a dinner party 5 people are to be seated around a circula   [#permalink] 01 Sep 2015, 21:06
Similar topics Replies Last post
Similar
Topics:
At a dinner party, 5 people are to be seated around a circular table. 5 06 Dec 2011, 20:11
At a dinner party, 5 people are to be seated around a 6 13 Jun 2011, 04:28
6 At a dinner party, 5 people are to be seated around a 11 17 Mar 2010, 06:01
9 At a dinner party, 5 people are to be seated around a circul 7 30 Oct 2009, 11:26
46 At a dinner party, 5 people are to be seated around a 12 26 Dec 2007, 07:16
Display posts from previous: Sort by