A computer programming team has 15 members.

(a) How many ways can a group of eight be chosen to work on a project?

(b) Suppose nine team members are women and six are men.

i. How many groups of eight can be chosen that contain four women and four men?

ii. How many groups of eight can be chosen that contain at least one man?

iii. How many groups of eight can be chosen that contain at most three women?

(c) Suppose two team members refuse to work together on projects. How many groups of

eight can be chosen to work on a project?

(d) Suppose two team members insist on either working together or not at all on projects.

How many groups of eight can be chosen to work on a project?