Final answer:
There are 56 different ways 8 athletes can finish first or second at a track meet, calculated using permutations where order matters.
Step-by-step explanation:
There are 8 athletes at a track meet, and we want to find out how many different ways they can finish first or second. This is a permutation problem, as the order in which they finish matters (first is different from second). To find this, we can use the formula for permutations of n objects taken r at a time, which is n! / (n-r)! In this case, n is 8 (the total number of athletes) and r is 2 (since we're looking for the first and second places).
Using the permutation formula:
- The number of ways the first place can be filled is 8 (since any of the 8 athletes could finish first).
- After the first place is taken, 7 athletes remain for the second place.
Therefore, the number of different ways for athletes to finish first or second is 8 ways for the first place × 7 ways for the second place = 56 different ways.