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

$1$

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