Answer: [tex]\dfrac{1}{6840}[/tex]
Step-by-step 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 = [tex]\dfrac{\text{favourable outcomes}}{\text{total ways}}[/tex]
[tex]=\dfrac{17!}{20!}\\\\=\dfrac{1}{20\times19\times18}\\\\=\dfrac{1}{6840}[/tex]
Hence, the required probability = [tex]\dfrac{1}{6840}[/tex]
