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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

At a dinner party, 5 people are to be seated around a [#permalink]

Show Tags

26 Dec 2007, 07:16

2

This post received KUDOS

9

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

5% (low)

Question Stats:

72% (01:16) correct
28% (00:23) wrong based on 503 sessions

HideShow timer Statistics

At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group?

1. we fix position of 1
2. we have 4*3=12 possible positions for left and right neighbors of 1.
3. for each position of x1y we have 2 possible positions for last two people: ax1yb and bx1ya.

OA is C, good...anyway, provided I am quite bad at combs, would you please explain it to me step by step in a very clear way..i cannot catch your 3 points!

OA is C, good...anyway, provided I am quite bad at combs, would you please explain it to me step by step in a very clear way..i cannot catch your 3 points!

let 1,2,3,4,5 are people.
"_ _ _ _ _" - positions

1. we fix position of 1
"_ _ 1 _ _"

2. we have 4*3=12 possible positions for left and right neighbors of 1.
"_ x 1 _ _" x e {2,3,4,5}. 4 variants "_ x 1 y _" y e {(2,3,4,5} - {x}. 3 variants total number of variants is 4*3=12

3. for each position of x1y we have 2 possible positions for last two people: ax1yb and bx1ya.
or "a x 1 y _" a e {(2,3,4,5} - {x,y}. 2 variants "a x 1 y b" b e {(2,3,4,5} - {x,y,a}. 1 variants

At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group?

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

Soln: Since the arrangement is circular and 2 seating arrangements are considered different only when the positions of the people are different relative to each other, we can find the total number of possible seating arrangements, by fixing one person's position and arranging the others.

Thus if one person's position is fixed, the others can be arranged in 4! ways. Ans is C.

At first lets see, there are how many cases to sit, if the they will sit not in round table. there are 5*4*3*2*1=5! cases And because it is no important that which sit is first that is mean that we must devise this to 5, prob=5!/5=4!=24

The solution Araik mentioned is logical as this was a problem with a round table. As a rule one needs to understand that there is a difference is arrangement in a row and that of a circle. Please refer to Math Workbook for 'COMBINATORICS'. Its explained very well there.

sort cut for any circular seating arrangements: (n-1)! =(5-1)! = 4! = 4*3*2*1 = 24

hi, kinda skeptical about the shortcut...do you really mean that when we see any circular table question, we can just plug in the (n-1)! formula?

So if it is a 8 table round table sitting arrangement, I can just use (8-1)! to get question resolved? Any other criteria or...does it limit only to certain criteria? Pls enlighten...many thanks!

sort cut for any circular seating arrangements: (n-1)! =(5-1)! = 4! = 4*3*2*1 = 24

hi, kinda skeptical about the shortcut...do you really mean that when we see any circular table question, we can just plug in the (n-1)! formula?

So if it is a 8 table round table sitting arrangement, I can just use (8-1)! to get question resolved? Any other criteria or...does it limit only to certain criteria? Pls enlighten...many thanks!

(n-1)! is correct for this constraint free question irrespective of the number of people in question. However, you may have to apply some logic if there are other constraints, such as A can't sit with B, OR D and E must sit together.
_________________

Re: At a dinner party, 5 people are to be seated around a [#permalink]

Show Tags

08 Jul 2013, 06:24

3

This post received KUDOS

At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group?

If the people sit in a row instead of a circular table, we would have 5*4*3*2*1 = 120 different combinations. But (restriction), if the people spin around the table without being in different position relative to each other does not generates a new position. Then, we have to eliminate ABCDE, BCDEA, CDEAB, DEABC and EABCD. Total: 5 arrangements. Then, instead of 5*4*3*2*1 = 120, we have to eliminate the 5 arrangements --> 5*4*3*2*1 = 24

After reading the solution given by walker, I thought in this one:

Fixing 1 person in the table (C for example), and moving the neighbours of this person.

Slots: 12345 --> We fix the third slot with person "C" --> 12C34--> then we have four possibilities for the slot 1 (person A, B, D or E), three possibilities for the second slot (ABDE less the person that we placed in the slot 1), two for the fourth slot and one for the last slot:

4*3*1*2*1 = 24
_________________

Encourage cooperation! If this post was very useful, kudos are welcome "It is our attitude at the beginning of a difficult task which, more than anything else, will affect It's successful outcome" William James

At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group?

If the people sit in a row instead of a circular table, we would have 5*4*3*2*1 = 120 different combinations. But (restriction), if the people spin around the table without being in different position relative to each other does not generates a new position. Then, we have to eliminate ABCDE, BCDEA, CDEAB, DEABC and EABCD. Total: 5 arrangements. Then, instead of 5*4*3*2*1 = 120, we have to eliminate the 5 arrangements --> 5*4*3*2*1 = 24

After reading the solution given by walker, I thought in this one:

Fixing 1 person in the table (C for example), and moving the neighbours of this person.

Slots: 12345 --> We fix the third slot with person "C" --> 12C34--> then we have four possibilities for the slot 1 (person A, B, D or E), three possibilities for the second slot (ABDE less the person that we placed in the slot 1), two for the fourth slot and one for the last slot:

4*3*1*2*1 = 24

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:

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...