The University of Ballygobackwards has three colleges: the College of Science, which has 12 staff, 8 of whom are female; the College of Engineering, which has 10 staff, 2 of whom are female; and the College of Arts, which has 20 staff, 9 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?
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