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 350,000 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:

Re: Circular Permutation Problem [#permalink]
26 Dec 2010, 07:59

Expert's post

1

This post was BOOKMARKED

subhashghosh wrote:

Hi

Could someone please help me with this, I am getting an answer 240. But I'm not sure if I'm correct.

Find the number of ways in which four men, two women and a child can sit at a table if the child is seated between two women.

Regards, Subhash

Note: 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 \((n-1)!\).

We have M, M, M, M, W, W, C --> glue two women and the child so that they become one unit and the child is between women: {WCW}. Now, these 5 units: {M}, {M}, {M}, {M}, {WCW} can be arranged around the table in (5-1)!=4! ways and the women within their unit can be arranged in 2 ways {W1, C, W2} or {W2, C, W1} so total # of arrangement is 4!*2=48.

Answer: 48.

240 would be the answer if the arrangement were in a row: {M}, {M}, {M}, {M}, {WCW} can be arranged in a row in 5! ways and the women within their unit can be arranged in 2 ways {W1, C, W2} or {W2, C, W1} so total # of arrangement is 5!*2=240.

Re: Circular Permutation Problem [#permalink]
26 Dec 2010, 08:23

Hi

Thanks for your reply. And I did not have the answer, so could not post it, apologies.

One question, if the places in table are numbered, wouldn't it become a case like arranging the members in the stated manner in a line, in which case the answer 240 is valid ?

Regards, Subhash _________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

Re: Circular Permutation Problem [#permalink]
26 Dec 2010, 08:48

Expert's post

subhashghosh wrote:

Hi

Thanks for your reply. And I did not have the answer, so could not post it, apologies.

One question, if the places in table are numbered, wouldn't it become a case like arranging the members in the stated manner in a line, in which case the answer 240 is valid ?

Regards, Subhash

If the chairs are numbered and one specific arrangement and the same arrangement but shifted by one position are considered different then the answer will simply be 48*7.

That's because 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. _________________

Re: Circular Permutation Problem [#permalink]
26 Dec 2010, 09:06

Bunuel wrote:

subhashghosh wrote:

240 would be the answer if the arrangement were in a row: {M}, {M}, {M}, {M}, {WCW} can be arranged in a row in 5! ways and the women within their unit can be arranged in 2 ways {W1, C, W2} or {W2, C, W1} so total # of arrangement is 5!*2=240.

For this szenario I received 744 different cases, including the cases when the child and a man or men are between the 2 women.

{M}, {M}, {M},{WCMW} 4*3*2*2*2=96 {M}, {M},{WCMMW} 3*2*3*2=72 {M},{WCMMMW}2*4*3*2*2=96 {WCMMMMW}5*4*3*2*2=240 These possibilities together with Bunuels possibilities when only the child is btw the women {WCW} gives 504+240=744

Re: Circular Permutation Problem [#permalink]
26 Dec 2010, 09:15

Expert's post

medanova wrote:

Bunuel wrote:

subhashghosh wrote:

240 would be the answer if the arrangement were in a row: {M}, {M}, {M}, {M}, {WCW} can be arranged in a row in 5! ways and the women within their unit can be arranged in 2 ways {W1, C, W2} or {W2, C, W1} so total # of arrangement is 5!*2=240.

For this szenario I received 744 different cases, including the cases when the child and a man or men are between the 2 women.

{M}, {M}, {M},{WCMW} 4*3*2*2*2=96 {M}, {M},{WCMMW} 3*2*3*2=72 {M},{WCMMMW}2*4*3*2*2=96 {WCMMMMW}5*4*3*2*2=240 These possibilities together with Bunuels possibilities when only the child is btw the women {WCW} gives 504+240=744

Please correct me if I am wrong!

I think the question means that ONLY the child must be between two women. _________________

Re: Circular Permutation Problem [#permalink]
20 Jan 2011, 08:38

Another great explanation. Thank you Bunuel

Bunuel wrote:

subhashghosh wrote:

Hi

Could someone please help me with this, I am getting an answer 240. But I'm not sure if I'm correct.

Find the number of ways in which four men, two women and a child can sit at a table if the child is seated between two women.

Regards, Subhash

Note: 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 \((n-1)!\).

We have M, M, M, M, W, W, C --> glue two women and the child so that they become one unit and the child is between women: {WCW}. Now, these 5 units: {M}, {M}, {M}, {M}, {WCW} can be arranged around the table in (5-1)!=4! ways and the women within their unit can be arranged in 2 ways {W1, C, W2} or {W2, C, W1} so total # of arrangement is 4!*2=48.

Answer: 48.

240 would be the answer if the arrangement were in a row: {M}, {M}, {M}, {M}, {WCW} can be arranged in a row in 5! ways and the women within their unit can be arranged in 2 ways {W1, C, W2} or {W2, C, W1} so total # of arrangement is 5!*2=240.

Re: Circular Permutation Problem [#permalink]
20 Jan 2011, 21:01

Expert's post

Another way to look at the question. (though let me point out first that the question doesn't specifically say 'circular table'. It just says 'sit at a table'. If it is a rectangular table, perhaps there are 4 chairs on one side, 3 on the other etc. Since you mentioned "Circular Permutation Problem" in the subject line, I am assuming it is meant to be a circular table.)

7 seats around a circular table, 7 people. First I make the child sit anywhere in 1 way since all seats are the same. The two women can sit around him in 2! ways. Now 4 seats are left for 4 men and they can occupy them in 4! ways. Total number of ways = 4!*2! = 48

Another thing, if the places are numbered, say 1, 2, 3 etc for the 7 seats, the number of arrangements will be 7*2!*4! = 336. Make the child sit on any one of the 7 seats since all are unique now. The women sit around the child in 2! ways and the men sit on the rest of the 4 seats in 4! ways. The reason why this number is greater than the number of arrangements in case of a row (240 ways) is because in a row, child cannot be in 1st or 7th position while in a circle, the child can sit on seat no 1 or seat no 7. So we have 2*2!*4! = 96 extra cases in case of numbered seats around a circular table. Note: 240 + 96 = 336 _________________

Re: Find the number of ways in which four men, two women and a [#permalink]
16 Aug 2014, 03:53

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. _________________

The Stanford interview is an alumni-run interview. You give Stanford your current address and they reach out to alumni in your area to find one that can interview you...

Originally, I was supposed to have an in-person interview for Yale in New Haven, CT. However, as I mentioned in my last post about how to prepare for b-school interviews...

Interested in applying for an MBA? In the fourth and final part of our live QA series with guest expert Chioma Isiadinso, co-founder of consultancy Expartus and former admissions...