anonymous
  • anonymous
There are 19 figure skaters in the Olympic women's competition, including 3 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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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kropot72
  • kropot72
With American #1 in first place there are 16P2 permutations with non-Americans as placegetters. With American #1 in second place there are 16P2 permutations with non-Americans as placegetters. With American #1 in third place there are 16P2 permutations with non-Americans as placegetters. Therefore there are 3 * 16P2 ways to award a medal to only American #1. There is the same number of ways to award a medal to only American #2 and to only American #3. Therefore the total number of ways to award the medals with one and only one American receiving a medal is given by\[9\times 16P2=3\times \frac{16!}{14!}=you\ can\ calculate\]

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