Question

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?

Answer 1

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

I hope this helps!