The first observation of the decays (B) over bar (0)(s) -> Ds+K-pi(+)pi(-) and (B) over bar (0)(s) -> Ds+K-pi(+)pi(-) are reported using an integrated luminosity of 1.0 fb(-1) recorded by the LHCb experiment. The branching fractions, normalized with respect to (B) over bar (0)(s) -> D-s(+)pi(-)pi(+)pi(-) and (B) over bar (0)(s) -> Ds+K-pi(+)pi(-), respectively, are measured to be B((B) over bar (0)(s)-> DsK-pi(+)pi(-))/B((B) over bar (0)(s)-> D-s pi(-)pi(+)pi(-)) = (5.2 +/- 0.5 +/- 0.3) x 10(-2) and B((B) over bar (0)(s)-> DsK-pi(+)pi(-))/B((B) over bar (0)(s)-> DsK-pi(+)pi(-)) = 0.54 +/- 0.07 +/- 0.07, where the first uncertainty is statistical and the second is systematic. The (B) over bar (0)(s) -> D-s(+) K-pi(+)pi(-) decay is of particular interest as it can be used to measure the weak phase gamma. First observation of the (B) over bar (0)(s) -> D-s1(2536)(+)pi(-), D-s1(+) -> D-s(+) pi(-)pi(+) decay is also presented, and its branching fraction relative to (B) over bar (0)(s) -> D-s(+) pi(-)pi(+)pi(-) is found to be B((B) over bar (0)(s) -> D-s1(2536)(+)pi(-),D-s1(+)-> D-s(+)pi(-)pi(+)/B((B) over bar (0)(s) -> D-s(+)pi(-)pi(+)pi(-))) = (4.0 +/- 1.0 +/- 0.4) x 10(-3). DOI: 10.1103/PhysRevD.86.112005