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circular permutations

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by Night reader » Tue Dec 07, 2010 3:30 pm
Seven men and seven women have to sit around a circular table so that no 2 women are together. In how many different ways can this be done?

A. 12!
B. 6!
C. 6*7!
D. 6!*7!
E. 14!
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by Bharat » Tue Dec 07, 2010 6:11 pm
Ans: D
For circular arrangements, the simple way is to fix the position/seat of anyone object/person & then try to calculate the possible arrangements for remaining objects/persons.

Begin with assuming that there are 14 chair around the table & obviously males/females will sit on alternate chairs.

Hence in this case fix the first position for a lady, & then remaining 6 ladies can be seated in only 6 alternating chairs, & can be seated in 6! ways.
For the remaining 7 men, we have 7 chairs, so possible arrangements are: 7!

Put together, all possible ways: 6!*7!.

Let me know if you have further questions.
Regards,
Bharat.
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by Night reader » Tue Dec 07, 2010 11:39 pm
thank yo Bharat, the explanation is clear.
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