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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...
Re: Seven men and seven women [#permalink]
19 Feb 2012, 04:47
This post received KUDOS
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
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]
20 Sep 2013, 00:07
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