Three research departments have 7 6 and 10 members respectiv

Three research departments have 7, 6, and 10 members, respectively. Each department is to select a delegate and alternate to represent the department at a conference. In how many ways can this be done?

Solution

For department containing 7 members,
number of ways of selecting delegate and alternate = 7*6 = 42

For department containing 6 members,
number of ways of selecting delegate and alternate = 6*5 = 30

For department containing 10 members,
number of ways of selecting delegate and alternate = 10*9 = 90

Total number of ways = 42 + 30 + 90 =162