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Thread: Not understanding the simplification of this factorial notation

  1. #1
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    Not understanding the simplification of this factorial notation

    Can someone please qualitatively explain the steps to get to this final answer I will give?

    The problem is 3^k*2^n-k / k!(n-k)! divided by 5^n/n! Note: n= k+(n-K)

    Somehow it is simplified to being (n choose K)*(0.6)^k*(0.4)^n-k

    Thank you all for considering my post!
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  2. #2
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    Re: Not understanding the simplification of this factorial notation

    $\dfrac{3^k \cdot 2^{n-k}}{\color{red}{k!(n-k)!}} \cdot \dfrac{\color{red}{n!}}{5^{k+(n-k)}}$

    $\displaystyle \color{red}{\binom{n}{k}} \cdot \dfrac{3^k \cdot 2^{n-k}}{5^k \cdot 5^{n-k}}$

    $\displaystyle \color{red}{\binom{n}{k}} \cdot \left(\dfrac{3}{5}\right)^k \cdot \left(\dfrac{2}{5}\right)^{n-k}$
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