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:

Just one question here.........since you will be seating the women also round the circular table, then why is that the logic of no. of asymmetric circular permutations of n objects does not apply here...?

since we have already arranged the 7 men in a circular fashion, the question, thereafter, ceases to be based on circular permutation.

[Tip :- when you consider such circular scenarios, imagine a "passing-the-parcel" game in either clockwise or anti-clockwise direction. the relative order in which the parcels are passed should be unique among all permutations]

Still not convinced?...have a look at my example in the attachment.
_________________

7 men can sit around a circular table in (7-1)! ways = 6! [Logic: no: of asymmetric circular permutations of n objects is (n-1)!.]

Next, all you need to do is seat the women in the vacant 7 slots (b/w the men) which can be done in 7! ways

so, my ans is (6! x 7!) ways

Are you sure about that??

Why are women not considerad also circular???

Yes, the solution given above is correct. Think of it this way: There are 7 men: Mr. A, Mr. B ..... and 7 women: Ms. A, Ms. B .... 14 seats around a circular table.

You seat the 7 women such that no two of them are together so they occupy 7 non-adjacent places in 6! ways. For the first woman who sits, each seat is identical. Once she sits, each seat becomes unique and when the next woman sits, she sits in a position relative to the first woman (e.g. 1 seat away on left, 3 seats away on right etc)

The 7 men have 7 unique seats to occupy. Each of the 7 seats are unique because they have a fixed relative position (e.g. between Ms. A and Ms. B or between Ms. C and Ms. B etc...). So the men can sit in 7! ways. Total 6!*7! ways.
_________________

7 men can sit around a circular table in (7-1)! ways = 6! [Logic: no: of asymmetric circular permutations of n objects is (n-1)!.]

Next, all you need to do is seat the women in the vacant 7 slots (b/w the men) which can be done in 7! ways

so, my ans is (6! x 7!) ways

Are you sure about that??

Why are women not considerad also circular???

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: n!/n=(n-1)!

Now, 7 men in a circle can be arranged in (7-1)! ways and if we place 7 women in empty slots between them then no two women will be together. The # of arrangement of these 7 women will be 7! and not 6! because if we shift them by one position we'll get different arrangement because of the neighboring men.

Re: Seven men and seven women have to sit around a circular [#permalink]

Show Tags

21 Sep 2013, 10:51

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: Seven men and seven women have to sit around a circular [#permalink]

Show Tags

13 Dec 2014, 22:08

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: Seven men and seven women have to sit around a circular [#permalink]

Show Tags

31 May 2016, 05:18

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: Seven men and seven women have to sit around a circular [#permalink]

Show Tags

12 Jul 2016, 06:00

But won't the women also be sitting in a circular manner, hence (7-1)!?

so shouldn't the answer be 6! x 6! ?

Bunuel wrote:

craky wrote:

idiot wrote:

7 men can sit around a circular table in (7-1)! ways = 6! [Logic: no: of asymmetric circular permutations of n objects is (n-1)!.]

Next, all you need to do is seat the women in the vacant 7 slots (b/w the men) which can be done in 7! ways

so, my ans is (6! x 7!) ways

Are you sure about that??

Why are women not considerad also circular???

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: n!/n=(n-1)!

Now, 7 men in a circle can be arranged in (7-1)! ways and if we place 7 women in empty slots between them then no two women will be together. The # of arrangement of these 7 women will be 7! and not 6! because if we shift them by one position we'll get different arrangement because of the neighboring men.

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...