Question

What is the probability that the top-three finishers in the contest will all be seniors?

Answer 1

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?

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In total, three students are taken from a set of 14, hence:

$C_{14,3} = \frac{14!}{3!11!} = 364$

Including only seniors, it would be three students from a set of 8, hence:

$C_{8,3} = \frac{8!}{3!5!} = 56$

Hence the probability is given by:

p = 56/364 = 0.1538 = 15.38%.

More can be learned about the combination formula at brainly.com/question/25821700

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