We present a measurement of the branching fractions of the 22 decay channels of the B0 and B+ mesons to D̅ (*)D(*)K, where the D(*) and D̅ (*) mesons are fully reconstructed. Summing the 10 neutral modes and the 12 charged modes, the branching fractions are found to be B(B0→D̅ (*)D(*)K)=(3.68±0.10±0.24)% and B(B+→D̅ (*)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 471×106BB̅ pairs collected at the Υ(4S) resonance with the BABAR detector at the SLAC National Accelerator Laboratory.
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