Number counts of galaxies are reanalyzed using a semianalytic model (SAM) of galaxy formation based on the hierarchical clustering scenario. We have determined the astrophysical parameters in the SAM that reproduce observations of nearby galaxies and used them to predict the number counts and redshifts of faint galaxies for three cosmological models: (1) the standard cold dark matter (CDM) universe, (2) a low-density flat universe with nonzero cosmological constant, and (3) a low-density open universe with zero cosmological constant. The novelty of our SAM analysis is the inclusion of selection effects arising from the cosmological dimming of the surface brightness of high-redshift galaxies and also from the absorption of visible light by internal dust and intergalactic H I clouds. Contrary to previous SAM analyses that do not take into account such selection effects, we find from comparison with observed counts and redshifts of faint galaxies in the Hubble Deep Field (HDF) that the standard CDM universe is not preferred, and a low-density universe either with or without a cosmological constant is favorable, as suggested by other recent studies. Moreover, we find that a simple prescription for the timescale of star formation (SF), being proportional to the dynamical timescale of the formation of the galactic disk, is unable to reproduce the observed number-redshift relation for HDF galaxies, and that the SF timescale should be nearly independent of redshift, as suggested by other SAM analyses for the formation of quasars and the evolution of damped Ly alpha systems.