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# Permutation Question

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In the Olympic women's skating competition, the gold medal goes to first place, silver to second, and bronze to third. If there are 15 skaters, including 4 Americans, in how many ways can the medals be awarded to three of the 15 skaters?

Sep 3, 2023

#1
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To find the number of ways the gold, silver, and bronze medals can be awarded to three of the 15 skaters, we can use combinations. We have 15 skaters to choose from, and we want to choose 3 of them for the medals.

The number of ways to choose 3 skaters out of 15 is given by the combination formula:

C(15, 3) = 15! / (3!(15 - 3)!) = 15! / (3! * 12!) = (15 * 14 * 13) / (3 * 2 * 1) = 455

So, there are 455 different ways to award the gold, silver, and bronze medals to three of the 15 skaters.

Sep 3, 2023
#3
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15 P 3  = 2730 ways       this is    15! / 12!       Or  15 for first choice * 14 for second * 13 for third = 2730

It would not be 15 C 3  because the order matters

Sep 3, 2023