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Math Help - binomial coefficent equation.

  1. #1
    Member integral's Avatar
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    binomial coefficent equation.

    I was watching a video playlist on applications of binomial coefficents and at the end of one of the videos it asked me to make an equation for them.
    This is what I got:


    \begin{pmatrix}<br />
n \\ <br />
r  <br />
\end{pmatrix}=\frac{1}{r!}}\prod_{i=0}^{r-1}(n-i)

    Reasoning: n choose r.
    say you have n people and you choose r, you at first have n people to choose from, then you have n-1 people to choose from, then n-2 people to choose from all the way to n-(r-1) because you start with n-0. But you have r! ways to arrange each group of people, so n(n-1)(n-2)...(n-(r-1)) also counts that r! ways to arrange each group of people. So we divide by r!

    leaving
    \begin{pmatrix}<br />
n \\ <br />
r  <br />
\end{pmatrix}=\frac{1}{r!}}\prod_{i=0}^{r-1}(n-i)

    This is correct?
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  2. #2
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