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Seven men and seven women have to sit around a circular

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Seven men and seven women have to sit around a circular [#permalink] New post 10 Nov 2004, 09:42
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Seven men and seven women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?

A. 5!*6!
B. 6!*6!
C. 5!*7!
D. 6!*7!
E. 7!*7!
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Feb 2014, 03:50, edited 1 time in total.
Edited the answer choices and added the OA
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 [#permalink] New post 10 Nov 2004, 10:27
I am unsure of this - after seeing the given answer choices. I dont get any of the answer choices and also way out from any of the ans choices.

Here is my understanding. I will be glad if someone can let me know the logical error I am committing here.

Putting one Man in a fixed position, the remaining men can be arranged in 6! ways.

For each arrangement, there are 7 positions for the women and they can be arranged in 7! ways.

Meaning the total arrangement is 7!*6! = 3628800 ways - only few hundred thousand ways more than the answer choices. Where am I going wrong?
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 [#permalink] New post 10 Nov 2004, 11:10
Thats a tough one.

We have to assume clock and anticlockwise arrangements are the same.
By saying that no two women must seat next to one another means that men and women must alternate in their sitting arrangements.

Let us take the example of 3 men [m1,m2,m3] and 3 women [w1,w2,w3]. That gives us (3-1)= 2 arrangements
[w1 m1 w2 m2 w3 m3 w1]
[w1 m2 w2 m1 w3 m3 w1]

Similarly for 7 men and 7 women we must have (7-1) = 6 combinations.

So i'd go for answer B. Anyway, that is how I would do it should this be an actual GMAT question.
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 [#permalink] New post 10 Nov 2004, 12:33
venksune wrote:
I am unsure of this - after seeing the given answer choices. I dont get any of the answer choices and also way out from any of the ans choices.

Here is my understanding. I will be glad if someone can let me know the logical error I am committing here.

Putting one Man in a fixed position, the remaining men can be arranged in 6! ways.

For each arrangement, there are 7 positions for the women and they can be arranged in 7! ways.

Meaning the total arrangement is 7!*6! = 3628800 ways - only few hundred thousand ways more than the answer choices. Where am I going wrong?


I checked this one venskune, and you are right. This is how even I did it. I have this book which is used for entrance exams ( those competitive exams). and this is how it ihas been done. The OAs are wrong...

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 [#permalink] New post 10 Nov 2004, 12:41
oxon wrote:
Let us take the example of 3 men [m1,m2,m3] and 3 women [w1,w2,w3]. That gives us (3-1)= 2 arrangements
[w1 m1 w2 m2 w3 m3 w1]
[w1 m2 w2 m1 w3 m3 w1]


Oxon for 3 men and 3 women example we actually have 12 ways.
Which follows the 3! * 2! = 12

Just rearranging the men we have 6 arrangements...
[w1 m1 w2 m2 w3 m3 w1]
[w1 m2 w2 m1 w3 m3 w1]
[w1 m3 w2 m2 w3 m1 w1]
[w1 m1 w2 m3 w3 m2 w1]
[w1 m2 w2 m3 w3 m1 w1]
[w1 m3 w2 m1 w3 m2 w1]
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 [#permalink] New post 10 Nov 2004, 12:48
IN The SAME way.. ( going by gayathris logic and oxons)... like i said earlier... its 7!*6!... the choices have to be wrong....

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 [#permalink] New post 10 Nov 2004, 16:09
I just want to say that I totally agree with Venksune's approach and I also came up with 7!*6!

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 [#permalink] New post 10 Nov 2004, 21:28
You're right guys... I got this from the following link, and it seems the answer choices are wrong :hammer

http://www.testmagic.com/forums/showthread.php?t=15259
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Re: [#permalink] New post 19 Feb 2012, 04:34
ComplexVision wrote:
You're right guys... I got this from the following link, and it seems the answer choices are wrong :hammer

http://www.testmagic.com/forums/showthread.php?t=15259


Yes, answer choices should be definitely wrong. I also agree with 6!7!

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Re: Seven men and seven women [#permalink] New post 19 Feb 2012, 04:47
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ComplexVision wrote:
Seven men and seven women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?

A. 24
B. 6
C. 4
D. 12
E. 3

I don't have the OA... Please help :wall


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.

So the answer is indeed 6!*7!.

Similar questions:
another-tricky-circular-permutation-problem-106928.html
circular-permutation-problem-106919.html
circular-table-106485.html
combinations-problem-104101.html
arrangements-around-the-table-102184.html
arrangement-in-a-circle-98185.html
please-help-with-the-seating-arrangement-problems-94915.html

Hope it helps.

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Re: Seven men and seven women have to sit around a circular [#permalink] New post 20 Sep 2013, 00:07
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Re: Seven men and seven women have to sit around a circular [#permalink] New post 06 Feb 2014, 08:22
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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).

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Hi Bumpot, I think what you could do for now is change the answer choices for this question so that we can answer it accordingly since the answer choices given don't make much sense

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Re: Seven men and seven women have to sit around a circular [#permalink] New post 07 Feb 2014, 03:50
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jlgdr wrote:
bumpbot wrote:
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.


Hi Bumpot, I think what you could do for now is change the answer choices for this question so that we can answer it accordingly since the answer choices given don't make much sense

Cheers
J


Thank you for the suggestion. Done.

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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Seven men and seven women have to sit around a circular   [#permalink] 07 Feb 2014, 03:50
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