SUMMARY
A model of random injections is defined which has domain A?BA\cup B and codomain A?CA\cup C, where AA, BB and CC are mutually disjoint finite sets such that |B|?|B|\leqslant |C|. The model encompasses both random permutations, which is the case B=C=\varnothingB=C=\varnothing, and random maximum matchings of a complete bipartite graph, which is the case A=\varnothingA=\varnothing. The possible components of random injections are cycles and paths. Results on the counts of cycles and paths of different sizes are obtained for this model.