  Using the topological technique of diagrams of spaces, we calculate the
homology of the union and the complement of finite arrangements of subspaces of
the form $D + SP^{n-d}(X)$ in symmetric products $SP^n(X)$ where $D\in
SP^d(X)$. As an application we include a computation of the homology of the
homotopy end space of the open manifold $SP^n(M_{g,k})$, where $M_{g,k}$ is a
Riemann surface of genus $g$ punctured at $k$ points, a problem which was
originally motivated by the study of commutative $(m+k,m)$-groups.
