The size distribution and the total density of clusters of a one-dimensional pure deposit can be expressed analytically from the Ising model. For a codeposit, the alloying effect and the presence of broken bonds at the cluster edges lead to inhomogeneities of the chemical composition of the clusters. We investigate the influence of codeposition on the size distribution of clusters in the case of an alloy that forms an ideal solution. We obtain the exact solution for the size distribution of clusters while the complete characterization of the system results from coupled analytical formulae in the grand-canonical ensemble. The results of this analytical model are successfully compared with those obtained by Monte Carlo simulations.