Twelve sprinters enter a race. In how many different ways can the gold, silver, and bronze medals be awarded?

1. Medal order matters, so this is a permutation of 12 runners taken 3 at a time. 2. Any of 12 sprinters can take gold, leaving 11 candidates for silver. 3. After gold and silver are fixed, 10 sprinters remain for bronze. 4. Multiply the options: 12 x 11 x 10 = 1,320 ways. 5. Option A, 220, is the combination count C(12, 3), which wrongly ignores the order of the medals. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.5 COUNTING PRINCIPLES_