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?

wiseowl Jan 15, 2024

#1**+1 **

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) **

ElectricPavlov Jan 15, 2024