The factors (1/N~1!)(1/N~2!) in equation 16.74 give an additive contribution to the Helmholtz potential that does not depend in any way on the forms of z1 and z2. Show that these factors lead to a ``mixing'' term in the entropy (not in the Helmholtz potential!) of the form
S~mixing=(−x1lnx1−x2lnx2)kB
This mixing term appears in fluids as well as in ideal gases. It accounts for the fact that the mixing of two fluids is an irreversible process (recall Example 2 of Section 4.5).