  We discuss how the $1/N_c$ expansion and the chiral random matrix theory
($\chi$RMT) can be used in the study of large-$N_c$ gauge theories. We first
clarify the parameter region in which each of these two approaches is valid:
while the fermion mass $m$ is fixed in the standard large-$N_c$ arguments ('t
Hooft large-$N_c$ limit), $m$ must be scaled appropriately with a certain
negative power of $N_c$ in order for the gauge theories to be described by the
$\chi$RMT. Then, although these two limits are not compatible in general, we
show that the breakdown of chiral symmetry can be detected by combining the
large-$N_c$ argument and the $\chi$RMT with some cares. As a concrete example,
we numerically study the four dimensional $SU(N_c)$ gauge theory with $N_f=2$
heavy adjoint fermions, introduced as the center symmetry preserver keeping the
infrared physics intact, on a $2^4$ lattice. By looking at the low-lying
eigenvalues of the Dirac operator for a massless probe fermion in the adjoint
representation, we find that the chiral symmetry is indeed broken with the
expected breaking pattern. This result reproduces a well-known fact that the
chiral symmetry is spontaneously broken in the pure $SU(N_c)$ gauge theory in
the large-$N_c$ and the large-volume limit, and therefore supports the validity
of the combined approach. We also provide the interpretation of the gap and
unexpected $N_c$-scaling, both of which are observed in the Dirac spectrum.
