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50! /(45! x5!)

Guest Feb 21, 2017

#1
+19054
+20

50! /(45! x5!)

$$\begin{array}{|rcll|} \hline && \frac{50!}{45!5!} \\ &=& \dbinom{50}{5} \\ &=& \frac{50}{5}\cdot \frac{49}{4}\cdot \frac{48}{3}\cdot \frac{47}{2}\cdot \frac{46}{1} \\ &=& \frac{50}{5}\cdot 49\cdot \frac{48}{12}\cdot \frac{47}{1}\cdot \frac{46}{2} \\ &=&10\cdot 49\cdot 4\cdot 47\cdot 23 \\ &=& \mathbf{2118760} \\ \hline \end{array}$$

heureka  Feb 21, 2017
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#1
+19054
+20

50! /(45! x5!)

$$\begin{array}{|rcll|} \hline && \frac{50!}{45!5!} \\ &=& \dbinom{50}{5} \\ &=& \frac{50}{5}\cdot \frac{49}{4}\cdot \frac{48}{3}\cdot \frac{47}{2}\cdot \frac{46}{1} \\ &=& \frac{50}{5}\cdot 49\cdot \frac{48}{12}\cdot \frac{47}{1}\cdot \frac{46}{2} \\ &=&10\cdot 49\cdot 4\cdot 47\cdot 23 \\ &=& \mathbf{2118760} \\ \hline \end{array}$$

heureka  Feb 21, 2017

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