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Twelve sprinters enter a race. In how many different ways can the gold, silver, and bronze medals be awarded?
A220 ways
B36 ways
C1,728 ways
D1,320 ways
Answer & Solution
Correct answer: D. 1,320 ways
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_
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