In combinatorics, combinatorial notation, e.g., C(n, r), is explicitly defined as a numerical value, a cardinality. Yet, we do not use another symbol to signify the set of outcomes--the collection of objects being referenced, whose cardinality is, for example, C(n, r). For an expert, this duality in notation, of signifying both cardinality and set, is not especially problematic; for a learner, however, it can be. This paper explores how combinatorial notation may, unintentionally, signify to learners something that does not lead to developing the conceptual, set-oriented ideas about combinatorics that experts have. Potential resolutions are discussed for combinatorics education.