  In the conventional approach to the $1/N_c$ expansion, electroweak
interactions are switched off and large $N_c$ QCD is treated in isolation. We
study the self-consistency of taking the large $N_c$ limit in the presence of
electroweak interaction. If the electroweak coupling constants are held
constant, the large $N_c$ counting rules are violated by processes involving
internal photon or weak boson lines. Anomaly cancellations, however, fix the
ratio of electric charges of different fermions. This allows a self-consistent
way to scale down the electronic charge $e$ in the large $N_c$ limit and hence
restoring the validity of the large $N_c$ counting rules.
