Multiplicity distributions of shower particles and target fragments in Li-Em (emulsion) collisions at 3 A GeV/c are experimentally studied. In the framework of the multisource thermal model, the multicomponent Erlang distribution is used to describe the experimental multiplicity distributions of shower particles, grey fragments, black fragments, and heavily ionized fragments. The correlations between these multiplicities are experimentally reported. With the increase of impacting centrality (or the target fragment multiplicity), a saturation phenomenon for shower particle multiplicity is observed in the experiment.