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Thread: Binomial Coeffients

  1. May 8th 2010, 01:08 PM #1
    tbone2500
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    Binomial Coeffients

    I have the following in my book:

    " (N K ) = n! / k! (n - k)!

    This formula is symmetric in k and n-k:

    ( N K ) = ( n / n - k)"

    I'm trying to understand what it means with 'this formula is symmetric in n and n-k'. I have tried to look for an answer, but haven't found anything. Does anyone know what that is supposed to mean?

    Can you explain it please?
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  2. May 8th 2010, 01:21 PM #2
    Plato
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    \binom{N}{K}=\frac{N!}{K!(N-K)!}
    \binom{N}{N-K}=\frac{N!}{(N-K)![N-(N-K)]!}=\frac{N!}{(N-K)!(K)!}
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  3. May 8th 2010, 02:03 PM #3
    tbone2500
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    So how can you just add a factorial to the second equation??
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  4. May 8th 2010, 02:56 PM #4
    Plato
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    Quote Originally Posted by tbone2500 View Post
    So how can you just add a factorial to the second equation??
    Actually it is a mere application of the combination formula and simple addition.
    You are expected to know how to use both.
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