The University of Ballygobackwards has three colleges:

• the College of Science, which has 12 staff, 7 of whom are female;
• the College of Engineering, which has 6 staff, 4 of whom are female;
• and the College of Arts, which has 20 staff, 8 of whom are female.

Each college has a Dean, who is chosen from the staff in that college. What is the total number of ways these three Deans can be chosen?

How many ways can three Deans be chosen, so that at least one of them is female?