Assignment:
At the first meeting of a committee to plan a Northern California pow-wow, there were 3 women and 3 men from the Miwok tribe, 2 men and 3 women from the Hoopa tribe and 4 women and 5 men from the Pomo tribe. If the ceremony subcouncil consists of 5 people, and it is randomly selected, find the probabilities that the subcouncil contains the following:
a. 3 men and 2 women
b. exactly 3 Miwoks and 2 Pomos
c. 2 Miwoks, 2 Hoopas, and 2 Pomos
d. exactly 3 Hoopas
Provide complete and step by step solution for the question and show calculations and use formulas.