A campus Goldfish Swallowing club chooses its officers Treas

A campus Goldfish Swallowing club chooses its officers (Treasurer, Aquariumist) completely at random, by lot. The club has 12 members. including Alfred and Bart. What is the probability that either Alfred is chosen Treasurer or Bart is chosen Aquariumist (or both)?

Solution

There are 11 ways in which Alfred is Treasurer, 11 ways in which Bart is Aquariumist and one in which both happen. Therefore there are 21 ways in which at least one happens. There are 12