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45!/(45-5)!5!

\(\begin{array}{|rcll|} \hline && \frac{45!}{(45-5)!5!} \\ &=& \dbinom{45}{5} \\ &=& \frac{45}{5}\cdot \frac{44}{4}\cdot \frac{43}{3}\cdot \frac{42}{2}\cdot \frac{41}{1} \\ &=& \frac{45}{15}\cdot \frac{44}{4}\cdot 43\cdot \frac{42}{2}\cdot \frac{41}{1} \\ &=& 3\cdot 11\cdot 43\cdot 21\cdot 41 \\ &=& \mathbf{1221759} \\ \hline \end{array}\)

5.625

   45!/(45-5)!5!=[45 x 44 x 43 x 42 x 41] / [5 x 4 x 3 x 2 x 1] =1,221,759.