Solutions - 5070-01

(a)

Apply the permutation formula for ordered selection:

$$\begin{array}{c}{(40)}_5=\frac{40!}{(40-5)!}\\ \\ \gg \gg 40\cdot 39\cdot 38\cdot 37\cdot 36\gg \gg \mathrm{78,960,960}\end{array}$$

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(b)

Apply the combination formula for unordered selection:

$$\begin{array}{c}\left(\genfrac{}{}{0px}{}{40}{5}\right)=\frac{40!}{5!(40-5)!}\\ \\ \gg \gg \frac{40\cdot 39\cdot 38\cdot 37\cdot 36}{5!}\gg \gg \mathrm{658,008}\end{array}$$