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Find the number of permutations of $2$ items from a set of $5$.
Hint: ${}^n \mathrm{P}_r = \dfrac{n!}{(n-r)!}$
${}^{5} \mathrm{P}_{2} = \dfrac{\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A1}}\hspace{54px}}~}!}{\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A2}}\hspace{54px}}~}!}$ ${}^{5} \mathrm{P}_{2} = \dfrac{5!}{3!}$
Cancel and calculate. Hint: Multiply the numbers down from $n$.
${}^{5} \mathrm{P}_{2} = \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{B1}}\hspace{35px}}~} \times \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{B2}}\hspace{35px}}~} = \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{BR}}\hspace{80px}}~}$ ${}^{5} \mathrm{P}_{2} = 5 \times 4 = 20$