In the olympic women's skating competition, the gold medal goes to first place, silver to second, and bronze to third. If there are skaters, including Americans, in how many ways can the medals be awarded to three of the skaters if exactly one of the americans wins a medal?
There are 6 possible ways the medals can be awarded to three of the skaters if exactly one of the Americans wins a medal:
1. American skater wins gold, non-American skater wins silver, non-American skater wins bronze
2. American skater wins gold, non-American skater wins bronze, non-American skater wins silver
3. Non-American skater wins gold, American skater wins silver, non-American skater wins bronze
4. Non-American skater wins gold, non-American skater wins silver, American skater wins bronze
5. Non-American skater wins silver, American skater wins bronze, non-American skater wins gold
6. Non-American skater wins bronze, American skater wins silver, non-American skater wins gold