couple problem

For discussing Olympiad Level Combinatorics problems
AntiviruShahriar
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couple problem

Unread post by AntiviruShahriar » Wed May 04, 2011 7:48 pm

৩টা কাপল ৬ জনের ১টা গোল টেবিলে বসবে। কতভাবে তারা বসতে পারে যেন প্রত্যেক স্বামী তার স্ত্রীর পাসে না বসে। [:D:D:D ha ha ha]

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nafistiham
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Re: couple problem

Unread post by nafistiham » Thu Nov 03, 2011 6:51 am

let us count the possibilities which do not satisfy the condition.
the total possibilities are $(6-1)!$
first let us fix the husbands.they can sit on $3$ chairs keeping a blank between every two of them.there can be only $2$ possibilities.now let us flip yje husbands with the wives and we get $2 \cdot 2$ which means the answers is
\[(6-1)!-4\]
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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