In a race in which 9 contestants are entered, in how many ways can the "first, second, and third" prizes be awarded?

Step 1 ：This is a permutation problem. In a race with 9 contestants, the first prize can be awarded in 9 ways (since there are 9 contestants), the second prize can be awarded in 8 ways (since one contestant has already won the first prize), and the third prize can be awarded in 7 ways (since two contestants have already won the first and second prizes). Therefore, the total number of ways the prizes can be awarded is \(9*8*7\).

Step 2 ：The total number of ways the prizes can be awarded is \(\boxed{504}\).