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.