Understanding combinatorics challenges in an upper-division thermodynamics course

Upper division thermodynamics courses require students to develop proficiency with several combinatorial topics. While little research has been done to establish student comfort and proficiency with these topics within physics, anecdotally, instructors of these courses report that students experience unaddressed challenges when working with combinatorics. Through examining student solutions to questions on homework assignments and examinations, we identified some common student difficulties with combinatorics in the context of an upper-division thermodynamics and statistical mechanics course at a large research university. Some of these common challenges include identifying how to work with distinguishability and order, checking formulas against a specific case, and combining the multiplicities of multiple systems.