How many ways can nine skiers finish in first second and third place?

The first-place finisher can be any one of the 9 skiers. For each of these choices, the second-place finisher can be any one of the remaining 8 skiers. For each of these choices, the third-place finisher can be any one of the remaining 7 skiers. So there are (9 x 8 x 7) = 504 ways in which the first, second, and third places can be comprised of members of the group of nine skiers.