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]

10 Nov 2004, 10:42

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

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10 Nov 2004, 11:27

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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10 Nov 2004, 12:10

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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10 Nov 2004, 13:33

venksune wrote:

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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10 Nov 2004, 13:41

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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10 Nov 2004, 13:48

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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10 Nov 2004, 17:09

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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10 Nov 2004, 22:28

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]

19 Feb 2012, 05:34

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]

19 Feb 2012, 05:47

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 [#permalink] 19 Feb 2012, 05:47

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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

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