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 [SOLVED] Binomial coefficients

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Bruno
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PostSubject: [SOLVED] Binomial coefficients   Sat Nov 07, 2009 6:34 pm

Here is a nice problem, in line with Mohammad's first combinatorial problem! Smile


Last edited by Bruno on Wed Nov 11, 2009 5:52 pm; edited 1 time in total
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Mohammad
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PostSubject: 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! . Very Happy
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Bruno
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PostSubject: Re: [SOLVED] Binomial coefficients   Sat Nov 07, 2009 7:31 pm

Good! cheers

Do you have a proof?
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Mohammad
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PostSubject: Re: [SOLVED] Binomial coefficients   Sat Nov 07, 2009 7:37 pm

Bruno wrote:
Good! cheers

Do you have a proof?
I don't get what you mean Surprised , proof is right up there Exclamation
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Mohammad
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PostSubject: 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 Wink
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Bruno
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PostSubject: Re: [SOLVED] Binomial coefficients   Sat Nov 07, 2009 7:52 pm

Good! That's also my solution. jocolor

Your other problem is quite hard! I will think about it.
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[SOLVED] Binomial coefficients
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