In the Olympic women's skating competition, the gold medal goes to first place, silver to second, and bronze to third. If there are 18 skaters, including 8 Americans, in how many ways can the medals be awarded to three of the 18 skaters?
There are 8 choices for the gold medalist, then 7 choices for the silver medalist and 6 choices for the bronze medalist for a preliminary count of $8 \times 7 \times 6 = \boxed{336}$ ways to distribute the medals.
To determine the number of ways the medals can be awarded, we need to use the concept of combinations.
Since there are 18 skaters in total, we have 18 options to choose from for the first-place gold medal. Once a skater is chosen for the gold medal, there are 17 remaining skaters to choose from for the second-place silver medal. Finally, for the third-place bronze medal, we have 16 remaining skaters to choose from.
Therefore, the number of ways the medals can be awarded is calculated as follows:
18 options for the gold medal * 17 options for the silver medal * 16 options for the bronze medal = 48,816 possible ways to award the medals.