Question

At a figure skating competition, the order of skaters is randomly selected. If

there are 20 skaters, what is the probability that Christie, Taylor, and Jona will
skate first, second, and third, respectively?

Answer 1

Answer:
`(1)/(6840)`

Explanation:

According to the permutations:

The arrangement of n things in an order = n!

If we fix that the first, second, and third person for skating, then we to arrange only 17 of the skaters.

Number of ways to arrange rest of 17 skaters = 17!

Number of ways that Christie, Taylor, and Jona will skate first, second, and third, respectively = 1 x 17!=17!

Number of ways to arrange all 20 skaters = 20!

Now, the required probability =
`\frac{\text{favourable outcomes}}{\text{total ways}}`

`=(17!)/(20!)\\\\=(1)/(20*19*18)\\\\=(1)/(6840)`

Hence, the required probability =
`(1)/(6840)`