We present a new and unique measurement of the branching fractions of b hadrons to states with 0, 1 and 2 open charm hadrons, using a sample of 350,000 Z's collected during the SLD/SLC 97-98 run. The analysis takes advantage of the excellent vertexing resolution of the VXD3, a pixel-based CCD vertex detector, which allows the separation of B and cascade D decay vertices. Analysis of the decay length distributions for each of the 1-, 2-, and 3-vertex topologies allows the extraction of the inclusive branching fractions. We measure: BR(b → 0D) =5.6% ± 1.1%(stat.) ± 2.0%(syst.), BR(b → 2D)= 24.6% ± 1.4%(stat.)± 4.0%(syst.) (preliminary), where b and D represent mixtures of open b and open c hadrons.