Using the combination formula, it is found that:
There are 364 different orders of top-three finishers that include all seniors.
The probability that the top-three finishers will all be seniors is 15.38%.
The order in which the players are taken is not important, hence the combination formula is used to solve this question.
What is the combination formula?
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In total, three students are taken from a set of 14, hence:
[tex]C_{14,3} = \frac{14!}{3!11!} = 364[/tex]
Including only seniors, it would be three students from a set of 8, hence:
[tex]C_{8,3} = \frac{8!}{3!5!} = 56[/tex]
Hence the probability is given by:
p = 56/364 = 0.1538 = 15.38%.
More can be learned about the combination formula at https://brainly.com/question/25821700
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