There are 15 figure skaters in the Olympic women's competition, including 4 Americans. The gold medal goes to first place, silver to second, and bronze to third.
Suppose that the Olympics powers-that-be decide that exactly one American must win a medal (no more and no less). Now how many ways are there to award the medals?
There are 4 ways to choose the American who gets the medal. There are then 11 skaters left, so there are 11 ways to award the second medal, then 10 ways to award the third medal, and two ways to order the last two medals, so the total number of ways is 4*11*10*2 = 880.