 Solution

The weak charged current spectator topology is $c\to q{W}^{+\ast }$, $W^{+\ast }\to u{\bar{q}}^{\prime }$, with the initial $\bar{u}$ a spectator. The pair $q\bar{u}$ forms the negative meson and $u{\bar{q}}^{\prime }$ the positive meson. The amplitude contains $V_{cq}^{\ast }{V}_{u{q}^{\prime }}$ in one common charged-current convention; complex conjugating all factors changes no rate classification. With $c_C=\cos {\theta }_C$ and $s_C=\sin {\theta }_C$, the CKM magnitudes areThus ${\pi }^{+}{K}^{-}$ is favoured, both equal-flavour pairs are singly Cabibbo suppressed, and $K^{+}{\pi }^{-}$ is doubly suppressed. The corresponding parametric rate hierarchy is $1:{\tan }^2{\theta }_C:{\tan }^4{\theta }_C$ after normalizing to the favoured mode. Cabibbo suppression counting alone does not rank the middle two: phase space, different matrix elements and hadronic final-state interactions matter. With identical constant matrix elements, the larger pion phase space would favour ${\pi }^{+}{\pi }^{-}$, whereas experimentally $K^{+}{K}^{-}$ is faster. The empirical decreasing order isAs a later cross-check, HFLAV's 2024 averages give approximately $4.00\%$, $0.411\%$, $0.149\%$ and $0.0138\%$ respectively. The exact middle ordering is an experimental input, not a consequence of the supplied masses and Cabibbo angle alone.^[ref]