+1678 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?
+36943 There are 2 Americans ...they can be either 1st 2nd 3rd = 6 ways
the 5 Canadians fill one of the two remaining spots = 10 ways 10 x 6 = 60 ways for ONE cnadian and ONE American to medal together
the final spot is then for one of the remaining 12
12 x 60 = 720 ways
If a Canadian or American can win the third spot , there are 17 skaters that can fill the third spot
17 x 60 = 1020 ways
(I think)
