  The dimensionality of the Hilbert space of a Chern-Simons theory on a 3-fold,
in the presence of Wilson lines carrying spin representations, had been counted
by using its link with the Wess-Zumino theory, with level $k$, on the 2-sphere
with points (to be called punctures) marked by the piercing of the
corresponding Wilson lines and carrying the respective spin representations. It
is shown, in the weak coupling (large $k$) limit, the formula decouples into
two characteristically distinct parts; one mimics the dimensionality of the
Hilbert space of a collection of non-interacting spin systems and the other is
an effective overall correction contributed by all the punctures. The exact
formula yield from this counting has been shown earlier to have resulted from
the consideration of the punctures to be distinguishable. We investigate the
same counting problem by considering the punctures to be indistinguishable.
Although the full formula remains undiscovered, nonetheless, we are able to
impose the relevant statistics for indistinguishable punctures in the
approximate formula resulting from the weak coupling limit. As an implication
of this counting, in the context of its relation to that of black hole entropy
calculation in quantum geometric approach, we are able to show that the
logarithmic area correction, with a coefficient of $-3/2$, that results in this
method of entropy calculation, in independent of whether the punctures are
distinguishable or not.
