Chapter 3 - Probability - Exercises 3.1 - 3.34 - Learning the Mechanics - Page 120: 3.12d

$1$

Combinations Rule $$\binom{N}{n} = \dfrac{N!}{n! (N-n)!}$$ ${\displaystyle{\binom{5}{0}} = \dfrac{5!}{0! \, (5-0)!} = \dfrac{5!}{0! \, 5!} = \dfrac{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)(5 \cdot 4 \cdot 3 \cdot 2 \cdot 1)}}$ ${\displaystyle{\binom{5}{0}} = \dfrac{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(1)(5 \cdot 4 \cdot 3 \cdot 2 \cdot 1)} = \boxed{1}}$