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[SOLVED] Binomial coefficients

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 Subject: [SOLVED] Binomial coefficients   Sat Nov 07, 2009 6:34 pm Here is a nice problem, in line with Mohammad's first combinatorial problem! Last edited by Bruno on Wed Nov 11, 2009 5:52 pm; edited 1 time in total

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 Subject: 10, Sec   Sat Nov 07, 2009 7:06 pm drinking water!Ans=the number of all subsets of A={X_1,...X_n,Y_1,...Y_n} which has n members= 2n!/n!n! .

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 Subject: Re: [SOLVED] Binomial coefficients   Sat Nov 07, 2009 7:31 pm Good! Do you have a proof?

Descartes

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 Subject: Re: [SOLVED] Binomial coefficients   Sat Nov 07, 2009 7:37 pm Bruno wrote:Good! Do you have a proof? I don't get what you mean , proof is right up there

Descartes

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 Subject: Another proof   Sat Nov 07, 2009 7:50 pm Sol2. You can also compare the coefficient of x^{n} in both sides of this equality (1+x)^{2n}=(1+x)^n(1+x)^n to get another proof

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 Subject: Re: [SOLVED] Binomial coefficients   Sat Nov 07, 2009 7:52 pm Good! That's also my solution. Your other problem is quite hard! I will think about it.