How many ways can this be done?

Question

Three research departments have 10, 6, and 8 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

Figure out how many ways you can select 2 from each department

Can select C From department 1 = x

10 2

Can select C From department 2 = y

6 2

Can select C From department 3 = z

8 2

Total number of ways = x * y * z