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:

In a round table the first person can be selected in 6 ways (any men or women can be selected), next one can be selected in 3 ways (i.e. opposite gender of the person selected in the first chair), next set can be taken by 2 remaining from an opposite gender from the 2nd chair, so 2 ways, 4th seat again can be filled by 2 remaining from opposite gender from the 3rd chair, last 2 chairs can be filled 1 way each. So no of ways:

Please draw a circle and mark 6 points on it. 3 x and 3 . 1)
a) split into 3 men and 3 women.
b) take men first -> first person can be seated in any of the available seats so # of ways -> 6
c) 2 men are remaining and only 2 seats are available. Since one man is fixed, adjacent positions cannot be occupied by men, also seat exactly opposite to first man cannot be occupied by any man. Thus we have only 2 places.
d) # of ways 2nd man can sit -> 2
e) last man has only one way.
f) 3 women are remaining and 3 places. 3 out of six have been occupied by 3 men.
g) First women can be placed in 3 ways
h] second women in 2 way and
i] third women in 1 way.

Three men can be seated first at the round table in 2! = 2 ways.
Then the three women can be seated in 3 gaps in 3! = 6 ways.
Hence the required number of ways = 2 x 6 = 12

I cannot give you an answer in terms of a equation. What I can do is explain it in a diagram. So if you draw a circle and draw six lines aorund that circle representing the six places where the people sit and then put man 1(m1), m2 and m3 in their place and the women between them. If you rotate the men (3 options) and you rotate the women (3 options) around the table you get a total 6 options. If you then switch the men and women and do the same you get another 6 and add these together you get 12 posibilities. I know it is crude but it worked for me. _________________

Three men can be seated first at the round table in 2! = 2 ways. Then the three women can be seated in 3 gaps in 3! = 6 ways. Hence the required number of ways = 2 x 6 = 12

Can you explain why the ways the men can be seated is 2! and not 3!

All - I thought it would be a good idea to put together [#permalink]
05 Jan 2005, 14:57

toddmartin wrote:

Can you explain why the ways the men can be seated is 2! and not 3!

Since I cannot attach any figures, refer to this URLfor explanation of circular permuations. This is my explanation...

1-2-3-4-5-6-1 (assume this to be a closed circle)

Lets assume the position of the first man to be "fixed" at 1, then there are two remaining positions for the remaining two men: 3rd and 5th seat.
Number of ways of seating a man in 3rd seat = 2
As only one man is left, number of ways of seating a man in 5th seat is 1.
Number of ways that three men can be seated first at the round table = 1*2*1=2

There are three remaining seats 2,4, and 6.
Number of options for 2 = 3
Number of options for 4 = 2 (only 2 women are left)
Number of options for 6 = 1 (only 1 woman left)
i.e. The three women can be seated in 3! ways = 6

In a round table the first person can be selected in 6 ways (any men or women can be selected), next one can be selected in 3 ways (i.e. opposite gender of the person selected in the first chair), next set can be taken by 2 remaining from an opposite gender from the 2nd chair, so 2 ways, 4th seat again can be filled by 2 remaining from opposite gender from the 3rd chair, last 2 chairs can be filled 1 way each. So no of ways:

6*3*2*2*1*1 = 72 ways. Is that correct ?[/quote]

Thx gayathri for the article, forgot abt circular prob, ofcourse, 72 needs to be divided by 6 ppl = 72/6 ==> 12 ways.

Another way of looking at..
The 1st person has 1 position only,not 6..On a circular table all the seats r the same..It doesn't make a lot of sense to get to 72 and then divide it by 6! Or so i think..
Good luck to all ..

In how many ways can 3 men and 3 women be seated around a [#permalink]
02 Jul 2015, 09:28

The answer GMAT wants is 12. You fix one guy to a seat and alternate man-woman. Now, the other two guys can be arranged in only two different ways with respect to that one guy you fixed in one seat. So, that's 2! ways. The women can be arranged in 3! ways with respect to the one guy. So, it's 2!*3!.

However

If each chair itself is unique, then shouldn't the answer be 72? The question assumes that the seats themselves don't matter, and that only the relative arrangement of people matters. So, if the seats actually mattered, say, seat A is a terrible chair that's about to fall apart, seat B is an Eames lounge chair, seat C is a massage chair, seat D is closest to the window, seat E is closest to the bathroom, and seat F is next to a different loud table, then such a scenario does exist, and the answer would need to be 72.

So, calculate 12 as you did above from one fixed guy in seat A, then move the guy you fixed to seat B, then C, then D, etc. That's 72 combinations, since each seat with respect to one guy has 12 arrangements and there are six seats total (12*6). Another way to do it is to think of each seat as M1-W2-M3-W4-M5-W6 (man seat#; woman seat#) around a table and multiply the combination, so after simplyfing it's 3*3*2*2*1*1 = 36. Those are only for the odd numbered seats for men, and even numbered seats for women, so the answer needs to be double that, giving us 72.

If 12 and 72 were both answer choices, I'd pick 12 but with serious protest. GMAT may ask for unique orders of people only, so the same order but in different chairs may be disqualified in GMAT's eyes. But, the GMAT doesn't specify that they want only unique orders of people - is it somehow implied in the question? The question itself is insufficient to draw a conclusion, esp. if 12 and 72 are both answer choices. Any thoughts?

gmatclubot

In how many ways can 3 men and 3 women be seated around a
[#permalink]
02 Jul 2015, 09:28

Hello everyone! Researching, networking, and understanding the “feel” for a school are all part of the essential journey to a top MBA. Wouldn’t it be great... ...

Are you interested in applying to business school? If you are seeking advice about the admissions process, such as how to select your targeted schools, then send your questions...

A lot of readers have asked me what benefits the Duke MBA has brought me. The MBA is a huge upfront investment and the opportunity cost is high. Most...