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Prove that nCk is a natural number

  1. Oct 24, 2009 #1
    1. The problem statement, all variables and given/known data

    Prove that [tex]\binom{n}{k}[/tex] is a natural number by showing that [tex]\binom{n}{k}[/tex] is the number of sets of exactly [tex]k[/tex] integers each chosen from [tex]1, ..., n[/tex].

    2. Relevant equations



    3. The attempt at a solution

    I posted a similar question before (https://www.physicsforums.com/showthread.php?t=339363) which asked for a proof by induction. This question is a bit different, and I'm not entirely sure how to get started. I'd appreciate some hints. Thanks.
     
  2. jcsd
  3. Oct 24, 2009 #2

    Dick

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    Here's your hint. How many different sequences (ordered!) of integers can you pick from the set {1,...,n}? Count sequences. Mull over that for a bit.
     
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