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

$21$

Combinations Rule $$\binom{N}{n} = \dfrac{N!}{n! (N-n)!}$$ ${\displaystyle{\binom{7}{2}} = \dfrac{7!}{2! \, 5!} = \dfrac{7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(2 \cdot 1)(5 \cdot 4 \cdot 3 \cdot 2 \cdot 1)}= \dfrac{7 \cdot 6}{2 \cdot 1}}$ ${\displaystyle{\binom{7}{2}} = \dfrac{7 \cdot 6}{2 \cdot 1} = \dfrac{42}{2} = \boxed{21}}$