Formulaic Maths Problems - get another problem: level 1, level 2, level 3 - link to this problem
Find the number of combinations of $1$ item from a set of $3$.
Hint: ${}^n \mathrm{C}_r = \dfrac{n!}{r! \, (n-r)!}$
${}^{3} \mathrm{C}_{1} = \dfrac{\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A1}}\hspace{54px}}~}!}{\class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A2}}\hspace{54px}}~}! \times \class{inputBox step1}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{A3}}\hspace{54px}}~}!}$ ${}^{3} \mathrm{C}_{1} = \dfrac{3!}{1! \times 2!}$
Cancel and calculate. Hint: Multiply the numbers down from $n$ in the numerator, and down from $r$ in the denominator.
${}^{3} \mathrm{C}_{1} = \dfrac{\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{B1}}\hspace{35px}}~}}{\class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{C1}}\hspace{35px}}~}} = \class{inputBox step2}{~\bbox[border:2px solid blue]{\strut\rlap{\class{inputReplace}{DR}}\hspace{80px}}~}$ ${}^{3} \mathrm{C}_{1} = \dfrac{3}{1} = 3$
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