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Proving binomial coefficients

  1. Sep 16, 2009 #1
    Here is the problem i am having trouble:

    Expressing the binomial coefficients in terms of factorials and simplifying algebraically show that

    (n over r) = (n-2+1)/r (n over r-1)

    i got that equals ((n-r+1)/r) ((n!)/((r-1)!(n-(r-1))!)) but i am trying to get that to equal n!/r!(n-r)! which would bring me back to (n over r)

    i am just getting confused on what to all do in between.
    hope i did no confuse anyone
  2. jcsd
  3. Sep 16, 2009 #2


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    Science Advisor

    I believe you have an error in the statement. The right hand side should read:
    (n-r+1)/r (n over r-1). However, you seem to have the next statement correct.

    To get the final result, note that r(r-1)! = r!
    Also (n-(r-1))!=(n-r+1)!=(n-r+1)(n-r)!
  4. Sep 16, 2009 #3
    ahh ok, thank you
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