Formulaic Maths Problems
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Find the number of permutations of $4$ items from a set of $8$.
Hint: ${}^n \mathrm{P}_r = \dfrac{n!}{(n-r)!}$
${}^{8} \mathrm{P}_{4} = \dfrac{\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A1}}\hspace{54px}}~}!}{\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A2}}\hspace{54px}}~}!}$
${}^{8} \mathrm{P}_{4} = \dfrac{[8]!}{[4]!}$
Cancel and calculate.
Hint: Multiply the numbers down from $n$.
${}^{8} \mathrm{P}_{4} = \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{B1}}\hspace{35px}}~} \times \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{B2}}\hspace{35px}}~} \times \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{B3}}\hspace{35px}}~} \times \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{B4}}\hspace{35px}}~} = \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{BR}}\hspace{80px}}~}$
${}^{8} \mathrm{P}_{4} = [8] \times [7] \times [6] \times [5] = [1680]$