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.