Question: A student council consists of 15 students.
a. In how many ways can a committee of six be selected from the membership of the council?
b. Two council members have the same major and are not permitted to serve together on a committee. How many ways can a committee of six be selected from the membership of the council?
c. Two council members always insist on serving on committees together. If they can't serve together, they won't serve at all. How many ways can a committee of six be selected from the council membership?
d. Suppose the council contains eight men and seven women.
(i) How many committees of six contain three men and three women?
(ii) How many committees of six contain at least one woman?
e. Suppose the council consists of three freshmen, four sophomores, three juniors, and five seniors. How many committees of eight contain two representatives from each class?