A linear compartmental model is a linear ODE model which can be visualized by a directed graph.  Identifiability is the study of determining whether a model’s parameter values can be inferred from the defining “input-output equation” under perfect conditions.  In this talk, I present a novel combinatorial formula for the computation of the coefficients of these input-output equations, and then completely classify the identifiability of a large class of linear compartmental models using this input-output equation characterization.