  Two-dimensional systems containing Ne electrons and Nh holes (Ne>Nh) strongly
correlated through Coulomb interactions in the presence of a large magnetic
field are studied by exact numerical diagonalization. Low lying states are
found to contain neutral (X0) and negatively charged (X-) excitons and higher
charged exciton complexes (Xk-, a bound state of k neutral excitons and an
electron). Representing these states in terms of angular momenta and binding
energies of the different exciton complexes, and the pseudopotentials
describing their interactions with electrons and with one another, permits
numerical studies of systems that are too large to investigate in terms of
individual electrons and holes. Laughlin incompressible ground states of such a
multi-component plasma are found. A generalized composite Fermion picture based
on Laughlin type correlations is proposed. It is shown to correctly predict the
lowest band of angular momentum multiplets for different charge configurations
of the system for any value of the magnetic field.
