I'm not being able to crack the following :S
$5$ couples are to be arranged in a circular table so that nobody sits beside his/her partner. In how many ways is this possible?
quick reply needed- circular permutation
"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor
Re: quick reply needed- circular permutation
You might want to check out Lucas problem of marriage couples. Removing some condition from that problem gives us this problem. So here is my solution (apologies in advance if it is wrong again!):
Note: The previous solution was wrong. I have checked this one with small values of $n$ and gives correct answer. Anyone got any other solution?
Last edited by abir91 on Fri Jan 28, 2011 12:53 pm, edited 1 time in total.
Reason: Fixed a bug in the previous solution
Reason: Fixed a bug in the previous solution
Re: quick reply needed- circular permutation
Sorry,i haven't read lucas' theorem.So what about my solution (a little bit confused)?
Suppose there is no condition for sitting.So we can make 10! ways for sitting.
Now suppose the couples have to sit by partners.That's time permutation is 32*5! (each couple makes 2!ways)
Therefore,10!-32*5! ways....
Please,post.If it is correct or not....
Suppose there is no condition for sitting.So we can make 10! ways for sitting.
Now suppose the couples have to sit by partners.That's time permutation is 32*5! (each couple makes 2!ways)
Therefore,10!-32*5! ways....
Please,post.If it is correct or not....
Try not to become a man of success but rather to become a man of value.-Albert Einstein
Re: quick reply needed- circular permutation
It is not correct as you have to deduct cases where there are less than five couples sitting together.
Note that, I did not mention anything about Lucas Theorem. It is about "Lucas's Problem of Marriage Couple", which is quite different from his many theorems.
Good try though. You are close, keep trying
Note that, I did not mention anything about Lucas Theorem. It is about "Lucas's Problem of Marriage Couple", which is quite different from his many theorems.
Good try though. You are close, keep trying
Re: quick reply needed- circular permutation
hey i guess i got it !!!
that doesn't matter only of 5 couples together permutation.we can get 4 couples together and one may be together or not and so on.....
we get 32*5!+16*6!+8*7!+4*8!+2*9! ways where 1 or more than 1 couple can get by partner.
so ans. is 10!-(32*5!+16*6!+8*7!+4*8!+2*9!)ways...
that doesn't matter only of 5 couples together permutation.we can get 4 couples together and one may be together or not and so on.....
we get 32*5!+16*6!+8*7!+4*8!+2*9! ways where 1 or more than 1 couple can get by partner.
so ans. is 10!-(32*5!+16*6!+8*7!+4*8!+2*9!)ways...
Try not to become a man of success but rather to become a man of value.-Albert Einstein
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Re: quick reply needed- circular permutation
i think it is 10!-(10*7)(8*5)(6*3)(4*1)(1*1)
Re: quick reply needed- circular permutation
Please explain
Try not to become a man of success but rather to become a man of value.-Albert Einstein