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Math Help - Combinatorial proof

  1. #1
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    Combinatorial proof

    By a combinatorial argument, prove that for r \leq n and r \leq m, \binom {n+m} {r} = \binom {m} {0} \binom {n} {r} + \binom {m} {1} \binom {n} {r-1} + ... + \binom {m} {r} \binom {n} {0}.
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  2. #2
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    Hint - To select r objects from (n+m) objects - break (n+m) objects in two groups (n) and (m) objects. How will you go about selecting r objects in total now (from both the groups)?
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