+1710 In the Olympic women's skating competition, the gold medal goes to first place, silver to second, and bronze to third. If there are 19 skaters, including 2 Americans and 5 Canadians, in how many ways can the medals be awarded to three of the 19 skaters so that an American wins a medal, and a Canadian wins a medal?
+23 We have 2 Americans and we can choose one of them to receive a medal. This can be done in 2 ways.
Choosing a Canadian to receive a medal:
We have 5 Canadians, and we can choose one of them to receive a medal. This can be done in 5 ways.
Choosing a third skater to receive a medal:
After selecting an American and a Canadian, we are left with 17 skaters (19 - 1 American - 1 Canadian). This can be done in 17 ways.
Thus, we have:2 (American's choice).×5(Canadian's choice)×17(third skater's choice)=170 ways
