Formulaic Maths Problems - get another problem: level 1, level 2, level 3 - link to this problem
Loading, please wait...
Find the number of permutations of $3$ items from a set of $4$.
Hint: ${}^n \mathrm{P}_r = \dfrac{n!}{(n-r)!}$
${}^{4} \mathrm{P}_{3} = \dfrac{\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A1}}\hspace{54px}}~}!}{\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A2}}\hspace{54px}}~}!}$ ${}^{4} \mathrm{P}_{3} = \dfrac{4!}{1!}$
Cancel and calculate. Hint: Multiply the numbers down from $n$.
${}^{4} \mathrm{P}_{3} = \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{B1}}\hspace{35px}}~} \times \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{B2}}\hspace{35px}}~} \times \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{B3}}\hspace{35px}}~} = \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{BR}}\hspace{80px}}~}$ ${}^{4} \mathrm{P}_{3} = 4 \times 3 \times 2 = 24$