Teaching abstract concepts is notoriously difficult, especially when we lack concrete metaphors that map to those abstractions. Combinatorix offers a novel approach that combines tangible objects with an interactive tabletop to help students explore, solve and understand probability problems. Students rearrange physical tokens to see the effects of various constraints on the problem space; a second screen displays the associated changes in an abstract representation, e.g., a probability tree. Using participatory design, college students in a combinatorics class helped iteratively refine the Combinatorix prototype, which was then tested successfully with five students. Combinatorix serves as an initial proof-of-concept that demonstrates how tangible tabletop interfaces that map tangible objects to abstract concepts can improve problem-solving skills.