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Need help in proving (by induction or by combinatorics) the following statement enter image description here

Is it possible to do it by induction? there are 3 veriables and I think I cannot easily do it by induction. Correct? I am not sure from where even to begin...

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  • $\begingroup$ We can in this case fix two of the variables, say $n$ and $r$ and do an induction on $m$. But the combinatorial argument is I think much clearer. $\endgroup$
    – André Nicolas
    Sep 18, 2014 at 3:34
  • $\begingroup$ Have a look here: math.stackexchange.com/questions/68564/… $\endgroup$
    – wckronholm
    Sep 18, 2014 at 3:34
  • $\begingroup$ You could also prove it by algebra, i.e., the binomial theorem. $\endgroup$
    – bof
    Sep 18, 2014 at 3:44
  • $\begingroup$ See also the posts that are Linked to the one above. And this catalog of binomial sums. $\endgroup$
    – user147263
    Sep 18, 2014 at 3:48

1 Answer 1

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See the Vandermonde Convolution Vandermonde

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  • $\begingroup$ Thank you man, you really helped! $\endgroup$
    – YohanRoth
    Sep 18, 2014 at 3:43

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