First observations of the decays A(b)(0) -> A(c)(+)D((s))(-) are reported using data corresponding to an integrated luminosity of 3 fb(-1) collected at 7 and 8 TeV center-of- ass energies in proton-proton collisions with the LHCb detector. In addition, the most precise measurement of the branching fraction B(B-s(0) -> D+Ds-) is made and a search is performed for the decays B-0((s)) -> A(c)(+)A(c)(-). The results obtained are B(A(b)(0) -> A(c)(+)D(-))/B(A(b)(0) -> A(c)(+)D(s)(-)) = 0.042 +/- 0.003 (stat) +/- 0.003 (syst), [B(A(b)(0) -> A(c)(+)D(s)(-))/B((B) over bar (0) -> D+Ds-)]/[B(A(b)(0) -> A(c)(+)pi(-))/B((B) over bar (0) -> D+pi(-))] = 0.96 +/- 0.02 (stat) +/- 0.06 (syst), B(B-s(0) -> D+Ds-)/B((B) over bar (0) -> D+Ds-) = 0.038 +/- 0.004 (stat) +/- (syst), B((B) over bar (0) -> A(c)(+)A(c)(-))/B((B) over bar (0) -> D+Ds-) < 0.0022[95% C.L.], B(B-s(0) -> A(c)(+)A(c)(-)) /B(B-s(0) -> D+Ds-) < 0.30[95% C.L.]. Measurement of the mass of the A(b)(0) baryon relative to the (B) over bar (0) meson gives M(A(b)(0)) ¿ M((B) over bar (0)) = 339.72 +/- 0.24 (stat) +/- 0.18 (syst) MeV/c(2). This result provides the most precise measurement of the mass of the A(b)(0) baryon to date.