Given a group of 4 computer science professors and 10 of their TAs:
(a) how many different 6 person soccer teams can be made?
(b) how many different 5 person teams can be made that contain at least 1 professor?
(c) how many different 8 person teams can be made that contain at least 2 professors and at least 4 TAs?
(d) how many different 4 person teams can be made that contain exactly 2 TAs?
Please show your work.