Question: In her past life, your instructor chaired a committee to choose a winner in an undergraduate math/science research paper contest. There were five judges on the committee ( from math, chemistry, physics, geology, and biology.) The first year of the contest there were five papers submitted. Each of the five judges read the papers and ranked them, with 1 being the best, 2 second-best, and so on. After all judges had read and ranked the papers, the committee met to decide on a winner. It happened that all five judges had the exact same rankings. If the five papers were equally meritorious, what is the probability that all five rankings would be the same? What do you conclude?