Using practical programming tasks to enhance combinatorial understanding

Probability theory has extensive applications across various domains, such as statistics, computer science, and finance. In probability education, students are introduced to fundamental principles which may include mathematical topics such as combinatorics and symmetric sample spaces. Students pursuing degrees in computer science possess a robust foundation in programming, software engineering, and algorithmic thinking. Despite entering probability courses with a unique perspective and learning potential, these students encounter challenges in grasping combinatorial concepts. In this experiment, we challenged first-year postsecondary computer science students to program a simulation of a practical combinatorics problem. Students commented on whether and how this task helped them internalize the basic concepts of combinatorics. We aim to show how utilizing programming tasks may empower students with a deeper grasp of combinatorics.