The multiplicity distributions of projectile fragments emitted in interactions of different nuclei with emulsion are studied by using a multi-source model.Our calculated results show that the projectile fragments can be described by the model and each source contributes an exponential distribution.As the weighted sum of the folding result of many exponential distributions,a multi-component Erlang distribution is used to describe the experimental data.The relationship between the height(or width)of the distribution and the mass of the incident projectile,as well as the dependence of projectile fragments on target groups,are investigated too.