Problem
The soon-to-be-famous scientist Ran Daman has an idea for an experiment. He will take a caffeinated sloth (dosed with 20mg of caffeine), place it on the ground, and observe which of m trees the sloth goes to first. Ran will perform this experiment n times, once for each of n sloths. Ran's hypothesis is that each sloth will select a tree uniformly at random and climb up that tree. For the questions below, assume that Ran's hypothesis is true. Also, concisely explain your reasoning.
At the end of the experiment, what is the expected number of trees which have at least two sloths?