Measurement of the ratios of branching fractions B(B0s --> Ds- pi+ pi+ pi-)/B(B0-->D- pi+ pi+ pi-) and B(B0s --> Ds- pi+)/B(B0-->D- pi+).

Using 355 pb;{-1} of data collected by the CDF II detector in pp[over ] collisions at sqrt[s]=1.96 TeV at the Fermilab Tevatron, we study the fully reconstructed hadronic decays B_{(s)};{0}-->D_{(s)};{-}pi;{+} and B_{(s)};{0}-->D_{(s)};{-}pi;{+}pi;{+}pi;{-}. We present the first measurement of the ratio of branching fractions B(B_{s};{0}-->D_{s};{-}pi;{+}pi;{+}pi;{-})/B(B;{0}-->D;{-}pi;{+}pi;{+}pi;{-})=1.05+/-0.10(stat)+/-0.22(syst). We also update our measurement of B(B_{s};{0}-->D_{s};{-}pi;{+})/B(B;{0}-->D;{-}pi;{+}) to 1.13+/-0.08(stat)+/-0.23(syst), improving the statistical uncertainty by more than a factor of 2. We find B(B_{s};{0}-->D_{s};{-}pi;{+})=[3.8+/-0.3(stat)+/-1.3(syst)]x10;{-3} and B(B_{s};{0}-->D_{s};{-}pi;{+}pi;{+}pi;{-})=[8.4+/-0.8(stat)+/-3.2(syst)]x10;{-3}.