Measurement of the B -> Dbar(*)D(*)K branching fractions

We present a measurement of the branching fractions of the 22 decay channels of the B0 and B+ mesons to Dbar(*)D(*)K, where the D(*) and Dbar(*) mesons are fully reconstructed. Summing the 10 neutral modes and the 12 charged modes, the branching fractions are found to be B(B0 -> Dbar(*)D(*)K) = (3.68 +- 0.10 +- 0.24)% and B(B+ -> Dbar(*)D(*)K) = (4.05 +- 0.11 +- 0.28)%, where the first uncertainties are statistical and the second systematic. The results are based on 429 fb^-1 of data containing 471.10^6 BBbar pairs collected at the Y(4S) resonance with the BaBar detector at the SLAC National Accelerator Laboratory.