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Possible Duplicate:
How to find a closed formula for the given summation

I am looking for a fast/best approach to compute $$\sum_{i=0}^{n} \binom{19}{i} \times \binom{7}{n-i}$$

For example,if $n=4$ the answer is $\binom{26}{4}$.Please explain your appraoch.

ADDED: After some experimentation with different numbers I think in general,$\sum_{i=0}^{n} \binom{p}{i} \times \binom{q}{n-i} = \binom{p+q}{n}$ holds.Does this result correct? If yes how could we proof this result.Any ideas?

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    Guess the rule then prove it.2011-09-05
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    See http://math.stackexchange.com/questions/47868/how-to-find-a-closed-formula-for-the-given-summation2011-09-05
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    @ Zev Chonoles:Thanks for the link :-)2011-09-05
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    @Zev Chonoles:You may delete this question,I think the other question has already provided me with sufficient information that one could possible want to know about this problem.Thanks.2011-09-05
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    @FoolForMath: I don't think there's a need to delete it, I will just close as duplicate.2011-09-05
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    @Zev Chonoles:That works for me.2011-09-05

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It comes very quickly.

This is just a way of finding out how many ways there are to choose n things from 26 objects. So for any n, the answer will be $26 \choose n$. How? Say we divide the 26 things into 2 groups, call 19 of them 'red' and 7 'blue.' Then we sum over the possibilities of taking 0 blue, n red or 1 blue, n-1 red, ... , n blue, 0 red. That is exactly your sum, and that is why it's just $26 \choose n$.