Highly multiplexed homogeneous in vitro screening assays for numerous possible nucleic acid targets, any of which might be present in a sample, utilize fluorescent hybridization probes that are combinatorially coded from a panel of fluorophores by subdividing each probe into portions and differently labeling each portion such that, when portions are combined, each probe has a unique code. The assays may include target amplification and real-time detection. Probe sets and kits containing additional assay reagents may be used to perform the screening assays.