Nine swimmers compete in a race. In how many ways can they finish first, second and third?

1. Order matters here, since first, second and third are different outcomes. 2. There are 9 candidates for first place. 3. Once first is settled, 8 remain for second place. 4. Once first and second are settled, 7 remain for third place. 5. Multiplying gives 9 times 8 times 7 = 504 ways. 6. Ignoring order would give 84, which counts the same three swimmers only once instead of in every finishing order. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.5 Counting Principles_