The university of ballygobackwards has three colleges: the college of science, which has 10 staff, 6 of whom are female; the college of engineering, which has 9 staff, 4 of whom are female; and the college of arts, which has 12 staff, 10 of whom are female. each college has a dean, who is chosen from the staff in that college.
how many ways can three deans be chosen, so that at least one of them is female?