First observation of the decays $\overline{B}^0 \to D^+ K^- \pi^+ \pi^-$ and $B^- \to D^0 K^- \pi^+ \pi^-$

First observations of the Cabibbo suppressed decays $\bar{B}^0\to D^+K^-\pi^+\pi^-$ and $B^-\to D^0K^-\pi^+\pi^-$ 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 ${\cal{B}}(\bar{B}^0\to D^+K^-\pi^+\pi^-)/{\cal{B}}(\bar{B}^0\to D^+\pi^-\pi^+\pi^-)=(5.9\pm1.1\pm0.5)\times10^{-2}$ and ${\cal{B}}(B^-\to D^0K^-\pi^+\pi^-)/{\cal{B}}(B^-\to D^0\pi^-\pi^+\pi^-)=(9.4\pm1.3\pm0.9)\times10^{-2}$, where the uncertainties are statistical and systematic, respectively. The $B^-\to D^0K^-\pi^+\pi^-$ decay is particularly interesting, as it can be used in a similar way to $B^-\to D^0K^-$ to measure the CKM phase $\gamma$.