Three research departments have 8, 7, and 6 members, respectively. Each department is to select a delegates and an alternate to represent the department at a conference. In how many ways can this be done?

There are four Olympians, Anne, Babaganoush, Carol, and David on the Canadian bobsledding team. As shown in the picture, all four members are needed to race at the same time. Only Babaganoush and Carol are qualified to be in the 1st position. Any member can fill the rest of the spots.   a.Determine the number of possible arrangements of the team

We are choosing participants for a panel discussion on allowing alcohol on a university campus. We must choose 2 administrators from a group of 8 administrators and 2 students from a group of 12 students. How many different panels can be formed?

The University of Ballygobackwards has three colleges: the College of Science, which has 15 staff, 5 of whom are female; the College of Engineering, which has 8 staff, 4 of whom are female; and the College of Arts, which has 17 staff, 6 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? Answer:   How many ways can three Deans be chosen, so that at least one of them is female? Answer: