A hockey club has 7 forwards, 5 defensemen, and 3 goalies. Each can play only in his designated subgroup. A coach chooses a team of 3 forwards, 2 defense, and 1 goalie.
a) How many different hockey teams can the coach assemble if position within the subgroup is not considered?
b) Players A, B and C prefer to play left forward, center, and right defense, respectively. What is the probability that these three players will play on the same team in their preferred positions if the coach assembles the team at random?