Flexible chiral molecules undergoing fast interconversion (on the NMR time scale) between different conformational enantiomers may yield "average" axial species with enantiotopically related sites. Contrary to the situation observed for rigid axial molecules, signals from these enantiotopic sites in NMR spectra recorded in chiral liquid-crystalline solvents can be resolved. In the present work, we studied the deuterium NMR spectra of tridioxyethylenetriphenylene (compound 4) statistically deuterated to 10% in the flexible side chains and dissolved in chiral and achiral Iyotropic liquid crystals based on poly(gamma-benzylglutamate). The fast chair-chair flipping of the side chains in 4 on average renders the molecule axially symmetric (D-3h) with pairs of enantiotopic ethylene deuterons. These deuterons exhibit unusually large enantiodiscrimination. To explain this observation, we first describe how the average symmetry of flexible molecules can be derived from the symmetry of the "frozen" conformers and the nature of the averaging process. The procedure is then applied to 4 and used to analyze the NMR results. It is shown that the large enantiodiscrimination in the present case reflects a large difference in the orientational ordering of the conformational enantiomers participating in the interconversion processes as well as a large geometrical factor due to the special shape of the dioxyethylene side groups. H-1 and C-13 NMR spectra of 4 in the same Iyotropic liquid crystalline solvent are analyzed to determine its ordering characteristics. Several related cases are also discussed.