The purpose of this article is to explore student-generated connections among counting problems. The literature indicates that such problems pose difficulties for students, who struggle to detect common structures and identify models of underlying problem types. A case study is presented here, in which students elaborate upon connections they make during the problem solving process. The selected case study highlights student work on three particular combinatorics problems, one of which highlights tendencies toward over-counting. The conception of Lobato ("Educational Researcher" 3(1):17-20, 2003) of actor-oriented transfer, in which students' (as opposed to experts') notions of similarity are emphasized, is used as a means by which to analyze the resulting qualitative data. Results include (1) a domain-specific categorization of fundamental types of actor-oriented transfer in combinatorics and (2) implications that there is much to be gained when students attend to features of problems that experts might not emphasize.