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Binomial theorem

  1. Jun 11, 2014 #1
    1. How do you get n!/(k-1)!(n-k+1)! from [tex]
    \begin{pmatrix}
    n\\k-1
    \end{pmatrix}
    [/tex]

    I thought it would be n!/(k-1)!(n-k-1)! where the n-k+1 on the bottom of the fraction would be a n-k-1 instead. I don't understand why there is a "+1" wouldn't you just replace k with k-1 in the binomial formula?
     
  2. jcsd
  3. Jun 11, 2014 #2
    [tex]\binom{n}{k-1}=\frac {n!}{(k-1)!(n-(k-1))!}=\frac{n!}{(k-1)!(n-k+1))!}[/tex]
     
  4. Jun 11, 2014 #3
    I just got it after i typed that out. I cant believe i didnt notice that
     
  5. Jul 17, 2014 #4
    Binomial theorem use for different purposes. The above person share write formula.
     
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