1. 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? 2. 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? Note: The two questions are different so look closely.

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Respuesta :

isyllus isyllus · Answer 1 · 2020-07-02T02:56:28+02:00

Answer:

1. 2730

2. 440

Step-by-step explanation:

Given that we have 15 skaters.

Number of Americans = 4

Number of other skaters = 11

1. Out of these 15, 3 medals are to be awarded.

Number of ways = ?

Number of possible ways for the first medal = 15

Number of possible ways for the second medal = 14

Number of possible ways for the third medal = 13

Required Number of ways = [tex]15 \times 14 \times 13[/tex] = 2730

2. Out of 15 medals, exactly 1 American wins medal and other 2 medals go to others. Number of ways = ?

Number of possible ways that one medal goes to an American = 4 (i.e. out of 4 Americans, one of them wins a medal)

Number of ways that other 2 medals go to others = [tex]11 \times 10[/tex] (others are 11)

Required Number of ways = [tex]4 \times 11 \times 10[/tex] = 440

So, the answers are:

1. 2730

2. 440