Three research departments have 9, 7, and 10 members, respectively. Each department is to select a delegate and an alternate to represent the department at a conference. In how many ways can this be done?
Work: First department: (They have 9 possibilities for delegate and 8 for alternate) 9 * 8 = 72 Second department: (They have 7 possibilities for delegate and 6 for alternate) 7 * 6 = 42 Third department: (They have 10 possibilities for delegate and 9 for alternate) 10 * 9 = 90 Total possibilities: 72 * 42 * 90 = 272,160 possibilities
