A coach has to form several teams of 3 athletes. 1 athlete can participate only in 1 team. What is the number of ways he can do that if:

Question

a) 6 athletes and teams have names: Team A and Team B

b) 6 athletes and teams do not have names

c) 9 athletes and teams are named A,B and C

Answer 1

From 6 athletes he can only pick 20 different teams.

In the first case he can assign those teams in 20*19 different ways.

In the second case, since the teams are for this purpose not distinguishable, he can only form 2 teams in 10*19 ways i.e. ₂₀C₂.

With 9 players he can form 84 teams and then assign them to teams in 84*83*82 ways.

If you don't understand how I arrived at these answers, you probably need a tutoring lesson which I would be willing to provide.