Measurements of the Absolute Branching Fractions of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>B</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mover accent="true"><mml:mi>c</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:mrow></mml:msub></mml:math>

A study of the two-body decays B^{±}→X_{cc[over ¯]}K^{±}, where X_{cc[over ¯]} refers to one charmonium state, is reported by the BABAR Collaboration using a data sample of 424 fb^{-1}. The absolute determination of branching fractions for these decays are significantly improved compared to previous BABAR measurements. Evidence is found for the decay B^{+}→X(3872)K^{+} at the 3σ level. The absolute branching fraction B[B^{+}→X(3872)K^{+}]=[2.1±0.6(stat)±0.3(syst)]×10^{-4} is measured for the first time. It follows that B[X(3872)→J/ψπ^{+}π^{-}]=(4.1±1.3)%, supporting the hypothesis of a molecular component for this resonance.