We provide a theoretical approach to determine the triple differential cross sections (TDCSs) for the ionization of molecules by single electron impact at low computational cost. This approach is based on the distorted wave (DW) method used within the first Born approximation (FBA). The short-range interaction between the ejected electron and the ionized target is explicitely taken into account. An important feature of this methodology is that it is applicable to any molecular target of known geometry. In this work, we determine the TDCSs of pyrimidine, the building block of some DNA and RNA nucleobases. The DW TDCSs are calculated for the ionization of five occupied orbitals and are compared with the available experimental data. In general, the DW TDCSs are in good agreement with the experimental data. This paper shows that the developed model can be easily applied to any molecule.