## Statistics (12th Edition)

$10$
The number of ways of selecting $n$ elements from $N$ elements is given by the combinations rule: $$\binom{N}{n} = \dfrac{N!}{n! (N-n)!}$$ The number of ways of selecting 2 elements from 5 elements is given by $$\binom{5}{2}$$ ${\displaystyle{\binom{5}{2}} = \dfrac{5!}{2! \, (5-2)!} = \dfrac{5!}{2! \, 3!} = \dfrac{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(2 \cdot 1)(3 \cdot 2 \cdot 1)}}$ ${\displaystyle{\binom{5}{2}} = \dfrac{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(2 \cdot 1)(3 \cdot 2 \cdot 1)} = \dfrac{5 \cdot 4}{2 \cdot 1} = \dfrac{20}{2} = \boxed{10}}$
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