# Combinatorics Problem: Selection of Job Applicants

• Shoney45
In summary, there are eight applicants for the job of dog catcher and three judges who each rank the applicants. The applicants are chosen if and only if they appear in the top three in all three rankings. The total number of ways the three judges can produce their three rankings is 175616. The probability of Mr. Dickens, one of the applicants, being chosen in a random set of three rankings is 27/512 or approximately 0.053, where C(n,r) = n!/r!(n-r)! and P(n,r) = n!/(n-r)!.

## Homework Statement

There are eight applicants for the job of dog catcher and three different judges who each rank the applicants.Applicants are chosen if and only 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 of Mr. Dickens, one of the applicants, being chosen in a random set of three rankings?

## Homework Equations

C(n,r) = n!/r!(n-r)! and P(n,r) = n!/(n-r)! Everything we are doing at this point involves these two formulas.

## The Attempt at a Solution

For (a), I think the total number of ways the three judges can produce their three rankings is
C(8,3)^3 = 175616.

For (b), if I pick Mr. Dickens, then that leaves me each judge with seven people to choose from, thus the amended equation becomes C(7,2)^3 = 9261, and the probability is 9261/175616 = 27/512 = 0.053

I think this is right, but I am not sure and would appreciate a second set of eyes on this one. Thanks for any help.

Last edited:
I just realized I didn't even read the problem correctly, and that I need to find a probability for (b). So I changed the result for (b). Sorry for any confusion.