  The division by N! in the expression of statistical entropy is usually
justified to students by the statement that classical particles should be
counted as indistinguishable. Sometimes, quantum indistinguishability is
invoked to explain it. In this paper, we try to clarify the issue starting from
Clausius thermodynamical entropy and deriving from it Boltzmann statistical
entropy for the ideal gas. This approach appears interesting for two reasons:
Firstly, it provides a direct heuristic link between thermodynamical and
statistical expressions of entropy that is missing in the usual approach. In
second place, it explicitly reminds that also statistical entropy is defined
with respect to a reference state, chosen to be the quantum-mechanical (T=0)
ground state of the N-particles in a box. Both factors $h^{3N}$ and $N!$ at the
denominator of the statistical entropy are a consequence of the quantum nature
of the reference state: in particular, the $N!$ is not related to the particle
identity, but to the identity of the boundary conditions on the
quantum-mechanical ground-state momenta, and to a general statistical
maximization principle. The introduction of a reference state also allows to
reinterpret the standard case of two mixing gases.
