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Updated on: 04 Aug 2019, 13:52
Originally posted by ComplexVision on 10 Nov 2004, 10:42.
Last edited by Bunuel on 04 Aug 2019, 13:52, edited 2 times in total.
Last edited by Bunuel on 04 Aug 2019, 13:52, edited 2 times in total.
Edited the answer choices and added the OA
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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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!
A. 5!*6!
B. 6!*6!
C. 5!*7!
D. 6!*7!
E. 7!*7!
19 Feb 2012, 05:47
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ComplexVision
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
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.
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.
20 Jan 2011, 21:31
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craky
idiot
7 men can sit around a circular table in (7-1)! ways = 6!
[Logic: no: of asymmetric circular permutations of n objects is (n-1)!.]
Next, all you need to do is seat the women in the vacant 7 slots (b/w the men) which can be done in 7! ways
so, my ans is (6! x 7!) ways
[Logic: no: of asymmetric circular permutations of n objects is (n-1)!.]
Next, all you need to do is seat the women in the vacant 7 slots (b/w the men) which can be done in 7! ways
so, my ans is (6! x 7!) ways
Are you sure about that??
Why are women not considerad also circular???
Yes, the solution given above is correct. Think of it this way:
There are 7 men: Mr. A, Mr. B .....
and 7 women: Ms. A, Ms. B ....
14 seats around a circular table.
You seat the 7 women such that no two of them are together so they occupy 7 non-adjacent places in 6! ways. For the first woman who sits, each seat is identical. Once she sits, each seat becomes unique and when the next woman sits, she sits in a position relative to the first woman (e.g. 1 seat away on left, 3 seats away on right etc)
The 7 men have 7 unique seats to occupy. Each of the 7 seats are unique because they have a fixed relative position (e.g. between Ms. A and Ms. B or between Ms. C and Ms. B etc...). So the men can sit in 7! ways.
Total 6!*7! ways.
:- when you consider such circular scenarios, imagine a "passing-the-parcel" game in 
