Let H=(V,E) be an r-uniform hypergraph of size n such that each edge of H meets at most d others. A finite map f:X->E induces a bipartite graph G H , f =(V f ,E f ) with vertex set V f =X Y, where Y= E, and with edge set E f ={{x,y}:x X,y f(x)}. We study matchings in the bipartite graph induced by a random f. The study was suggested by consideration of the call sequence acceptance behavior of a load-sharing system for cellular telephone networks, invented by Matula and Yang.