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Combinatorial Identity

  • Thread starter Pietjuh
  • Start date
Can someone help me how to deal with this identity that i must prove?

[tex]{n + k-1 \choose n - 1} = \sum_{i=1}^k {k-1\choose i -1} {n \choose i}[/tex]

I've tried to figure out what the combinatorial meaning of the right hand side is, but I didn't succeed :(
I think it will help to rewrite it in the form:

[tex]{n + k-1 \choose k} = \sum_{i=1}^k {k-1\choose k - i} {n \choose i}[/tex]

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