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The first observation of the decays $\bar{B}^0_{s}\to D_s^+K^-\pi^+\pi^-$ and$\bar{B}^0\to D_s^+K^-\pi^+\pi^-$ are reported using an integrated luminosityof 1.0 fb$^{-1}$ recorded by the LHCb experiment. The branching fractions,normalized with respect to $\bar{B}^0_{s}\to D_s^+\pi^-\pi^+\pi^-$ and$\bar{B}^0_{s}\to D_s^+K^-\pi^+\pi^-$, respectively, are measured to be{\br(\bar{B}^0_{s}\to D_s^+K^-\pi^+\pi^-)\over\br(\bar{B}^0_{s}\toD_s^+\pi^-\pi^+\pi^-)} &= (5.2\pm0.5\pm0.3)\times10^{-2}, {\br(\bar{B}^0\toD_s^+K^-\pi^+\pi^-)\over\br(\bar{B}^0_{s}\to D_s^+K^-^\pi^+\pi^-)} &=0.54\pm0.07\pm0.07, where the first uncertainty is statistical and the secondis systematic. The $\bar{B}^0_{s}\to D_s^+K^-\pi^+\pi^-$ decay is of particularinterest as it can be used to measure the weak phase $\gamma$. Firstobservation of the $\bar{B}^0_s\to D_{s1}(2536)^+\pi^-, D_{s1}^+\toD_s^+\pi^-\pi^+$ decay is also presented, and its branching fraction relativeto $\bar{B}^0_{s}\to D_s^+\pi^-\pi^+\pi^-$ is found to be {\br(\bar{B}^0_s\toD_{s1}(2536)^+\pi^-, D_{s1}^+\to D_s^+\pi^-\pi^+)\over\br(\bar{B}^0_{s}\toD_s^+\pi^-\pi^+\pi^-)} &= (4.0\pm1.0\pm0.4)\times10^{-3}.

First observation of the decays $\bar{B}^0_{(s)}\to D_s^+K^-\pi^+\pi^-$ and $\bar{B}^0_s\to D_{s1}(2536)^+\pi^-$