We have a club consisting of 6 distinct men and 5 distinct women:

a. In how many ways can we select a committee of 5 persons?

b. In how many ways can we select a committee of five persons consisting of three men and two women?

c. In how many ways can we select a committee of five persons that has at most one man?

d. In how many ways can we select a committee of five persons that has at least two women?

e. Club members Jana and Ben are in a relationship. In how many ways can we select a committee of five persons so that Jana and Ben serve together?

f. Jana and Ben have had a fight and do not want to serve on the committee together, so in how many ways can we select a committee of five that do not contain BOTH Jana and. Ben?