An exactly solvable quantum many-fermion system with an arbitrarily strong two-body interaction is studied and some exact thermodynamic functions (in the thermodynamic limit) are derived within the framework of the statistical inference scheme based on information theory. The solution for the associated su(3) Clebsch-Gordan series (for any number of particles) is given. A very important relation between the (many-body) system`s entropy per particle (in the thermodynamic limit) and the multiple Kronecker product multiplicities (for any member of an infinite class of Lie-algebraic exactly solvable models) is demonstrated. A general procedure for the treatment of the full class of solvable models is outlined.Facultad de Ciencias Exactas