Nine swimmers race and the one named Ariel is known to have won first place. In how many ways can the first three places then be filled?

1. First place is already decided, so it contributes 1 option rather than 9. 2. That leaves 8 swimmers who could take second place. 3. After second is filled, 7 remain for third. 4. Multiplying gives 1 times 8 times 7 = 56 ways. 5. Using 9 times 8 for the remaining places would give 72, which forgets that Ariel is no longer available lower down. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.5 Counting Principles_