  We have used the CLEO II detector to study the multiplicity of charged
particles in the decays of B mesons produced at the $\Upsilon(4S)$ resonance.
Using a sample of 1.5 x 10^6 B meson pairs, we find the mean inclusive charged
particle multiplicity to be 10.71 +- 0.02 +0.21/-0.15 for the decay of the
pair. This corresponds to a mean multiplicity of 5.36 +- 0.01 +0.11/-0.08 for a
single B meson. Using the same data sample, we have also extracted the mean
multiplicities in semileptonic and nonleptonic decays. We measure a mean of
7.82 +- 0.05 +0.21/-0.19 charged particles per $B\bar{B}$ decay when both
mesons decay semileptonically. When neither B meson decays semileptonically, we
measure a mean charged particle multiplicity of 11.62 +- 0.04 +0.24/-0.18 per
$B\bar{B}$ pair.
