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Combinatorics Proof

  1. Aug 26, 2004 #1
    Hello all

    In my calculus book, this problem has been pestering me"

    Prove nC(k-1) + nCk = (n+1)Ck, where k > 0 which is read " n choose k-1" + "n choose k"

    = n+1C k.

    I tried using the formula for the binomial coefficient, but it becomes very messy. I also tried setting k = 1, but then it did not seem like I was actually proving it. Rather I was showing that the statement holds for k > 0. Would I have to use proof my induction? Any replies would be greatly appreciated.

    Thanks a lot
  2. jcsd
  3. Aug 26, 2004 #2


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    Use the definition of nCk in terms of factorials. Use the fact that n! = n(n-1)! OR alternatively, (n+1)! = (n+1)n!. Start from the LHS and don't stop till you get the RHS :biggrin:
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