6. (13 marks)

6 Teachers and 12 students volunteer for a committee to discuss extra-curricular activities. How many committees of 5 people can be made if:

1. a) there are no restrictions
2. b) there must be 3 students on the committee
3. c) there must be no more than 2 teachers on the committee
4. d) there must be at least one teacher and at least one student on the committee
5. e) Barry and Miss Morrison cannot be on the committee together.