In anisotropic layered films of a multicomponent n-Bi1.92In0.02Te2.85Se0.15 solid solution in strong magnetic fields from 2 to 14 T at low temperatures, quantum oscillations of the magnetoresistance associated with the surface states of electrons in three-dimensional topological insulators are studied. From analysis of the spectral distribution of the amplitudes of quantum magnetoresistance oscillations, the main parameters of the Dirac-fermion surface states are determined. The results are compared with data obtained by the method of scanning tunneling spectroscopy. It is shown that a high surface concentration determines the contribution of the Dirac-fermion surface states to the thermoelectric properties of n-Bi1.92In0.02Te2.85Se0.15 films.