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There are 15 skaters in the Olympic women's competition, including 4 Americans. The gold medal goes to first place, silver to second, and bronze to third. In how many ways can the medals be awarded to three of the 15 skaters, if exactly one of the Americans wins a medal?

Respuesta :

Answer:

1320 ways

Step-by-step explanation:

First we have 4 americans and 11 non-americans, so for one medal, the number of possibilities for americans is 4.

Then, for a second medal, we want a non-american, so there are 11 possibilities.

For the third medal, we have only 10 possibilities, as one non-american has already got the second medal.

As the american can win any of the three positions, we also need to multiply the probabilities by a combination of 3 choose 1: C(3,1) = 3

So the number of ways that exactly one american wins a medal is:

3 * 4 * 11 * 10 = 1320 ways

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