A group of friends Anna (A), Bjorn (B), Candice (C), David (D) and Ellen (E) want to enter a basketball contest that caters for teams of different sizes. A team with n players is called an n-team. A player can be in several different teams, including teams of the same size. There is a restriction however: players in a 2-team cannot play together in any larger team. For example, if friends A, B,C, D form the teams AB, BCD, ACD, then they cannot also form the teams BD or ABC, among others. a) List all different 3-teams that the friends could enter.

b) What is the maximum number of teams that the friends can enter if they want to include exactly two 3-teams and at least one 2-team, but no other size teams.

c) What is the maximum number of teams that the friends can enter if they want to include exactly three 3-teams and at least one 2-team, but not other size teams.

d) The five friends want to enter 8 teams including at least one 2-team and at least one 3-team and no team of any other size. Find three ways of doing this with a different number of 3-teams in each case.