then box all final answers. 1. There are 12 athletes joining the Baguio Marathon Event. How many ways can the first, second, and third placers be chosen?
Answer:
To find the number of ways the first, second, and third placers can be chosen from 12 athletes, we can use the permutation formula:
\[ P(n, r) = \frac{n!}{(n - r)!} \]
Where:
- \( n \) is the total number of athletes (12 in this case)
- \( r \) is the number of placers (3 in this case)
- \( ! \) denotes factorial, which means the product of all positive integers up to that number
Plugging in the values:
\[ P(12, 3) = \frac{12!}{(12 - 3)!} \]
\[ P(12, 3) = \frac{12!}{9!} \]
\[ P(12, 3) = \frac{12 \times 11 \times 10 \times 9!}{9!} \]
\[ P(12, 3) = 12 \times 11 \times 10 \]
\[ P(12, 3) = 1320 \]
Therefore, there are \( \boxed{1320} \) ways the first, second, and third placers can be chosen from 12 athletes.