Determination of the Number of Generations of Quarks and Leptons from Flavor-Color Symmetry

It is shown that the fact that there are six flavor-color degrees of freedom (two flavors in each generation, three colors, and lepton number) implies, under plausible assumptions, that there are three generations of light quarks and leptons. The assumptions include (a) supersymmetry for the preon theory, (b) validity of the chiral group $\mathrm{SU}{\mathrm{}\left(4\right)\mathrm{}}_L\otimes \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\otimes \mathrm{SU}{\mathrm{}\left(4\right)\mathrm{}}_R\otimes \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_R$ at the stage prior to the generation of the quark and lepton masses, and (c) chiral symmetry and the supersymmetric Nambu-Goldstone mechanism to protect quarks and leptons from getting large masses.