Random endangered things

This page gives the solutions to questions raised in this blog post.

Suppose 13 teams each select an endangered thing from a list of 10 things. If every endangered is equally likely to be selected each time, what is the probability that one endangered thing will be selected 5 or more times? Before doing any calculations, my guess was around 1 percent Turns out the correct probability is more than 6 percent. When I simulated 1,000,000 selections, there were 64,065 in which the most popular item was selected 5 or more times, around 6.4%.

How likely is it that every item will be selected at least once? From 1,000,000 simulations, the probability appears to be around 1.4%.

I imagine most people would be more surprised by one item being selected 5 or more times than they would be by every item appearing at least once, even though the former is between 4 and 5 times more likely.