Hello,
I am totally stumped, and hope that someone can point me in the right direction.
Imagine that there are 70 applicants for a job. Four committee members independently create a top-ten list from the applicant pool.
I believe there are 70! / (70 - 10)! possible lists. But what I am stumped by is the question of the probability of there being differing amounts of overlap between the lists, assuming that they were created randomly.
For example, what is the probability that only one of the 70 applicants will appear on all fours lists, assuming they were created independently and randomly? Or what is the probability that no applicants will appear on all four lists (independently and randomly created)? I've been drawing multinomial trees all morning for scaled-down versions of this situation to see if I can generate a solution that I can scale up, but to no avail. So I'm hoping that someone out there can either solve this for me or at least point me in the right direction.
Thank you!
I am totally stumped, and hope that someone can point me in the right direction.
Imagine that there are 70 applicants for a job. Four committee members independently create a top-ten list from the applicant pool.
I believe there are 70! / (70 - 10)! possible lists. But what I am stumped by is the question of the probability of there being differing amounts of overlap between the lists, assuming that they were created randomly.
For example, what is the probability that only one of the 70 applicants will appear on all fours lists, assuming they were created independently and randomly? Or what is the probability that no applicants will appear on all four lists (independently and randomly created)? I've been drawing multinomial trees all morning for scaled-down versions of this situation to see if I can generate a solution that I can scale up, but to no avail. So I'm hoping that someone out there can either solve this for me or at least point me in the right direction.
Thank you!