  We study the scaling of kaon decay amplitudes with the number of colours,
$N_c$, in a theory with four degenerate flavours, $N_f=4$. In this scenario,
two current-current operators, $Q^\pm$, mediate $\Delta S=1$ transitions, such
as the two isospin amplitudes of non-leptonic kaon decays for $K\to
(\pi\pi)_{I=0,2}$, $A_0$ and $A_2$. In particular, we concentrate on the
simpler $K\to\pi$ amplitudes, $A^\pm$, mediated by these two operators. A
diagrammatic analysis of the large-$N_c$ scaling of these observables is
presented, which demonstrates the anticorrelation of the leading ${\mathcal
O}(1/N_c)$ and ${\mathcal O}(N_f/N_c^2)$ corrections in both amplitudes. Using
our new $N_f=4$ and previous quenched data, we confirm this expectation and
show that these corrections are $naturally$ large and may be at the origin of
the $\Delta I=1/2$ rule. The evidence for the latter is indirect, based on the
matching of the amplitudes to their prediction in Chiral Perturbation Theory,
from which the LO low-energy couplings of the chiral weak Hamiltonian, $g^\pm$,
can be determined. A NLO estimate of the $K \to (\pi\pi)_{I=0,2}$ isospin
amplitudes can then be derived, which is in good agreement with the
experimental value.
