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Five women are to be seated around a table. Then five men

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Konstantin Lynov
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Five women are to be seated around a table. Then five men [#permalink] New post   08 Aug 2003, 01:05
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Five women are to be seated around a table. Then five men are to be assigned positions next to a woman. In how many ways can couples thus be arranged, if only the relative order around the table is of importance?



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Re: Five women are to be seated around a table. Then five men [#permalink] New post   08 Aug 2003, 03:06
if only the relative order around the table is of importance...

I assume that we do not need to eliminate a rotation factor
5!*5!
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Re: Five women are to be seated around a table. Then five men [#permalink] New post   08 Aug 2003, 15:15
stolyar wrote:
if only the relative order around the table is of importance...

I assume that we do not need to eliminate a rotation factor
5!*5!


First, if "only the relative order around the table is of importance" then you must surely eliminate the rotation factors.

Second, even if your assumption was correct, your answer would be wrong. You have only considered the number of permutations should the women be in the odd (or even) position and the men in the other, even (or odd) positions. You need to multiply this by 2 in order to get them all.

Then if you need to eliminate the rotations, divide by 10. You will end up with 5! x 4!, the same result you would get if you were to pick one person as an anchor.
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Re: Five women are to be seated around a table. Then five men [#permalink] New post   08 Aug 2003, 22:57
4! *5! is right when we need to place men and women ALTERNATELY around the table. However, the question as is worded is not perhaps clear on this account and only says that every man should be beside a woman. Therefore a circular combo like ...wwwmmwmmwm... will also be ok . Are we missing something Aka ?
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Re: Five women are to be seated around a table. Then five men [#permalink] New post   09 Aug 2003, 02:09
No Stolyar - You ARE our angel ! Please revert on the question I had posed.
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Re: Five women are to be seated around a table. Then five men [#permalink] New post   09 Aug 2003, 03:51
anupag wrote:
4! *5! is right when we need to place men and women ALTERNATELY around the table. However, the question as is worded is not perhaps clear on this account and only says that every man should be beside a woman. Therefore a circular combo like ...wwwmmwmmwm... will also be ok . Are we missing something Aka ?


You are right, that is a possibility. There are so many typos that I tend to assume more that the question poses at times.
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Re: Five women are to be seated around a table. Then five men [#permalink] New post   09 Aug 2003, 06:00
AkamaiBrah wrote:
anupag wrote:
4! *5! is right when we need to place men and women ALTERNATELY around the table. However, the question as is worded is not perhaps clear on this account and only says that every man should be beside a woman. Therefore a circular combo like ...wwwmmwmmwm... will also be ok . Are we missing something Aka ?


You are right, that is a possibility. There are so many typos that I tend to assume more that the question poses at times.


Here's my answer:

There are five couples to be seated. Fix one. Then the rest can be arranged in 4! ways around the table. Each couple itself can be arranged in 2! ways.

Therefore the answer is 4!*2!=48 ways.

Konstantin, comments ?
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Re: Five women are to be seated around a table. Then five men [#permalink] New post   18 Aug 2003, 21:29
anupag wrote:
4! *5! is right when we need to place men and women ALTERNATELY around the table. However, the question as is worded is not perhaps clear on this account and only says that every man should be beside a woman. Therefore a circular combo like ...wwwmmwmmwm... will also be ok . Are we missing something Aka ?


KL, are you sure this is the solution? I ask because anupag's point is still unanswered - "....a circular combo like ...wwwmmwmmwm... will also be ok ...."
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Konstantin Lynov
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Re: Five women are to be seated around a table. Then five men [#permalink] New post   19 Aug 2003, 10:02
Well... the book says it is 5!*4!



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Re: Five women are to be seated around a table. Then five men [#permalink]
19 Aug 2003, 10:02
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