# Probability and counting techniques

A gold medal, a silver medal, and a bronze medal will be awarded to the first, second, and third place finishers in a 10K road race.

Of the 100 entrants, 20 are from the Buffalo New York team.

Determine the number of ways that the Buffalo team could have at least 2 of the top 3 finishers.

You want at least $2$ of the winners to be from the BNY team, so that would be $\binom{20}{2}\binom{80}{1}$. And you also have $\binom{20}{3}$ as the option where all of the winners are from the BNY team.