There are 60 runners in a race. How many ways can the runners finish first, second, and third?
There are $\square$ different ways that the runners can finish first through third. (Type a whole number.)

Step 1 ：We are given that there are 60 runners in a race. We want to find out how many ways the runners can finish first, second, and third.

Step 2 ：This is a permutation problem. We have 60 runners and we want to know how many ways we can arrange 3 of them (first, second, and third place).

Step 3 ：The formula for permutations is: \(P(n, r) = \frac{n!}{(n-r)!}\), where n is the total number of items, r is the number of items to choose, and '!' denotes factorial (the product of all positive integers up to that number).

Step 4 ：In this case, n = 60 and r = 3.

Step 5 ：Substituting the values into the formula, we get \(P(60, 3) = \frac{60!}{(60-3)!}\).

Step 6 ：Calculating the above expression, we find that there are 205320 different ways that the runners can finish first through third.

Step 7 ：Final Answer: There are \(\boxed{205320}\) different ways that the runners can finish first through third.