First Observation of the Decays B¯⁰ → D⁺K^-π⁺π^- and B^- → D⁰K^-π⁺π^-

First observations of the Cabibbo-suppressed decays B¯⁰ → D⁺K^-π⁺π^- and B^- → D⁰K^-π⁺π^- are reported using 35 pB^-1 of data collected with the LHCb detector. Their branching fractions are measured with respect to the corresponding Cabibbo-favored decays, from which we obtain B(B¯⁰→ D⁺K^-π⁺π^-)/B(B¯⁰→D⁺π^-π⁺π^-)=(5.9±1.1±0.5)×10^-2 and B(B^-→D⁰K^-π⁺π^-)/B(B^-→ D⁰π^-π⁺π^-)=(9.4±1.3±0.9)×10^-2, where the uncertainties are statistical and systematic, respectively. The B^- → D⁰K^-π⁺π^- decay is particularly interesting, as it can be used in a similar way to B^- → D⁰K^- to measure the Cabibbo-Kobayashi-Maskawa phase γ.