There are 15 figure skaters in the Olympic women's competition, including 4 Americans. The gold medal goes to first place, silver to second, and bronze to third.
Suppose that the Olympics powers-that-be decide that exactly one American must win a medal (no more and no less). Now how many ways are there to award the medals?
There are 3 groups of skaters as follows:
4 x 11 x 10 =440 ways. But 1st, 2nd and 3rd prizes can be awarded in 3! =6 ways.
Therefore, there are: 440 x 6 =2,640 ways.
Hi answering guest,
I think that you have double counted.
lets assume there are 2 prizes. Non americans get both. there would be 11 ways for the first one to be allocated and 10 ways for the second one.
So that is 110 ways to place the non americans in realtion to EACH OTHER
Now the american has to be slotted in. There is 4 to choose from and 3 places to chose from (infront, in middle, or at back)
So that is 12 ways the americans can be slotted in
Altogether I think there are 110*12 = 1320 ways.