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Compute:  85 choose 82

Mr.Owl  Oct 20, 2017
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 #1
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85nCr82 =98,770

Guest Oct 20, 2017
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Compute:  85 choose 82

 

\(\begin{array}{|rcll|} \hline && \mathbf{\binom{85}{82}} \\\\ &=& \binom{85}{85-82} \\\\ &=& \binom{85}{3} \\\\ &=& \dfrac{85}{3}\cdot \dfrac{84}{2}\cdot \dfrac{83}{1} \\\\ &=& 85\cdot \dfrac{84}{2\cdot 3}\cdot 83 \\\\ &=& 85\cdot \dfrac{84}{6}\cdot 83 \\\\ &=& 85\cdot 14 \cdot 83 \\\\ &\mathbf{=}&\mathbf{ 98770 } \\ \hline \end{array}\)

 

laugh

heureka  Oct 20, 2017

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