Final answer:
To determine the total number of ways swimmers can finish first, second, and third in a race with 8 swimmers, you multiply the number of choices for each position. The order matters, so you use permutations, resulting in 8 x 7 x 6 = 336 different ways.
Step-by-step explanation:
To figure out how many different ways the swimmers can finish first, second, and third in a race with 8 swimmers, we need to use permutations because the order in which the swimmers finish is important. We are looking to fill 3 distinct positions: first, second, and third, and we have 8 different swimmers to choose from for these positions.
Using the formula for permutations:
- The number of ways to choose the first place swimmer is 8 (since any of the 8 swimmers can come in first).
- Once the first place has been chosen, 7 swimmers remain for the second place.
- Then, there are 6 swimmers left for third place.
Thus, the total number of permutations is found by multiplying these possibilities together: 8 × 7 × 6 = 336 different ways.
Combinations are not used in this scenario because they are relevant when the order does not matter, which is not the case here.