This problem is about dividing the class of 65 people random

This problem is about dividing the class of 65 people randomly into two teams.

(a) Suppose the two teams have 33 and 32 people each. What is the probability that Conan, Drew, and Kylie (three particular people) are on the same team?

(b) Now suppose that, in order to even up the teams, I join \"the class\" and we separate the class randomly into two teams of 33 each. Now what is the probability these three particular people are on the same team?

[Hint: you have to think carefully about whether there is overcounting in (b) or not.]

Solution