Measurement of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mo>*</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mi>D</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mo>*</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><mml:mi>K</mml:mi></mml:math>branching fractions

We present a measurement of the branching fractions of the 22 decay channels of the ${B}^{0}$ and ${B}^{+}$ mesons to ${\overline{D}}^{(*)}{D}^{(*)}K$, where the ${D}^{(*)}$ and ${\overline{D}}^{(*)}$ mesons are fully reconstructed. Summing the 10 neutral modes and the 12 charged modes, the branching fractions are found to be $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{\overline{D}}^{(*)}{D}^{(*)}K)=(3.68\ifmmode\pm\else\textpm\fi{}0.10\ifmmode\pm\else\textpm\fi{}0.24)%$ and $\mathcal{B}({B}^{+}\ensuremath{\rightarrow}{\overline{D}}^{(*)}{D}^{(*)}K)=(4.05\ifmmode\pm\else\textpm\fi{}0.11\ifmmode\pm\else\textpm\fi{}0.28)%$, where the first uncertainties are statistical and the second systematic. The results are based on $429\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data containing $471\ifmmode\times\else\texttimes\fi{}{10}^{6}B\overline{B}$ pairs collected at the $\ensuremath{\Upsilon}(4S)$ resonance with the BABAR detector at the SLAC National Accelerator Laboratory.

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