Proof

Question: How many 2-letter words start with a, b, or c and end with either y or z?

Answer 1: There are two words that start with a, two that start with b, two that start with c, for a total of \(2+2+2\text{.}\)

Answer 2: There are three choices for the first letter and two choices for the second letter, for a total of \(3 \cdot 2\text{.}\)

Since the two answers are both answers to the same question, they are equal. Thus \(2 + 2 + 2 = 3\cdot 2\text{.}\)