  We study the $N_c$ scalings of pion-nucleon and nucleon-nucleon scatterings
and find that a consistent large $N_c$ counting can be established if we assume
Witten's counting rules are applied to matrix elements or scattering amplitudes
which use the relativistic normalization for the nucleons. With the pionless
effective field theory, we also find that the $S$-wave nucleon-nucleon
interaction is so strong that it should be treated nonperturbatively at the
leading order in the $1/N_c$ expansion. By summing all the leading order
diagrams, we find that the deuteron binding energy is of order $1/N_c$. In
contrast, meson-meson interaction is so weak that loosely-bound meson-meson
molecular states may not exist in the large $N_c$ limit.
