  We study the scaling with the number of colours, $N_c$, of the weak
amplitudes mediating kaon mixing and decay. We evaluate the amplitudes of the
two relevant current-current operators on the lattice for $N_c=3-7$. We
conclude that the subleading $1/N_c$ corrections in $\hat{B}_K$ are small, but
those in the $K \rightarrow \pi\pi$ amplitudes are large and fully
anti-correlated in the $I=0, 2$ isospin channels. We briefly comment on the
implications for the $\Delta I=1/2$ rule.
