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## Homework Statement

There are eight applicants for a job, and three different judges who each rank the three applicants. Applicants are chosen if an donly if they appear in the top three in all three rankings.

a) How many ways can the three judges produce their three rankings?

b) What is the probability tha tMr. Dickens, one of the applicants, being chosen in a random set of three rankings?

## Homework Equations

P(n,r) and C(n,r)

## The Attempt at a Solution

a) = 3 * C(8,3)

b) I am feeling really uneasy about my solution, but I think that if a judge picks Mr.

Dickens, then he has C(7,2) ways to pick the remaining applicants. So the probability

of Mr. Dickens being chosen in a random set of three rankings is [3*C(7,2)]/[3*C(8,3)]