Fun in teaching counting using the powerball lottery

One of the many challenges in teaching a required course in discrete mathematical structures to students in computing-related curricula is undoubtedly the teaching of counting techniques and their applications. Traditionally, a technique-driven approach is often adopted in which basic counting principles are introduced one at a time and then unrelated examples are used to illustrate the application of each counting principle. Unfortunately, students often mistake each cleverly constructed solution as a "trick" and fail to understand the underlying counting principle involved under different conditions. In this paper, we propose a problem-driven approach using the powerball lottery and its variations. By examining how numbers can be selected, fundamental counting principles such as the sum and product rules, permutations and combinations, the pigeonhole principle, and other counting principles can easily be introduced and explored. Using this approach, we are able to motivate our students to study and enjoy doing counting.