We prepared silica-dye-nanocrystal hybrid particles and studied the energy transfer from semiconductor nanocrystals (= donor) to organic dye molecules (= acceptor). Multishell CdSe/CdS/ZnS semiconductor nanocrystals were adsorbed onto monodisperse Stober silica particles with an outer silica shell of thickness 2-23 nm containing organic dye molecules (Texas Red). The thickness of this dye layer has a strong effect on the energy transfer efficiency, which is explained by the increase in the number of dye molecules homogeneously distributed within the silica shell, in combination with an enhanced surface adsorption of nanocrystals with increasing dye amount. Our conclusions were underlined by comparison of the experimental results with numerically calculated FRET efficiencies and by control experiments confirming attractive interaction between the nanocrystals and Texas Red freely dissolved in solution.