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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?

 Dec 17, 2019
 #1
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There are 4 ways to choose the American who gets the medal.  There are then 11 skaters left, so there are 11 ways to award the second medal, then 10 ways to award the third medal, and two ways to order the last two medals, so the total number of ways is 4*11*10*2 = 880.

 Dec 17, 2019
 #2
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huh thats what i thought too but its incorrect

Guest Dec 17, 2019
 #3
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maybe try to give the medals to americans first

Guest Dec 17, 2019
 #4
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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.

 Dec 17, 2019

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