Challenge Level

A chess club has $10$ members, $4$ women and $6$ men, of whom two are brothers.

A team of $4$ members is selected to play a match. Suppose that each member has an equal chance of being selected what is the probability that both brothers are in the team and what is the probability that neither brother is in the team?

What is the probability that there are at least two women in the team and what is the probability that there are at least two men in the team?