“I got a rock” and a probability question along with it (part 1)

For the quantitative reasoning course I teach at the University of Tennessee, all of the instructors work together to create a bank of problems we all build our exams from. Typically we each include a bonus question on our exams, and one of the problems we conceived seemed worth breaking down in a blog post. It’s about finding the probability of tossing rocks into buckets in a certain way.

Here’s the question: Six rocks are put into three buckets at random, with no bucket left empty. Find the probability that at least…