A method for detecting aneuploidy, the method comprising: providing a first set of oligonucleotide binders and a second set of oligonucleotide binders, each of the oligonucleotide binders comprising: a 5' region comprising a first universal primer site; a 3' region comprising a second universal primer site; and a central region, wherein the central region of the oligonucleotide binders of the first set comprise target-specific sequences that bind to different regions on a target nucleic acid comprising chromosome 21 and a first code site, and the central region of the oligonucleotide binders of the second set comprise reference specific sequences that bind to different regions on a reference nucleic acid comprising a chromosome other than chromosome 21 and a second code site; exposing the sets of oligonucleotide binders to a sample pool comprising the target nucleic acid and the reference nucleic acid, wherein the first set binds to multiple regions on the target nucleic acid and the second set binds to multiple regions on the reference nucleic acid; removing the unbound oligonucleotide binders; diluting and compartmentalizing the sample in a plurality of droplets at a dilution sufficient that most of the droplets contain no more than a single target or reference nucleic acid bound to binders from the exposing step the droplets further comprising primer species that bind to the universal primer sites and first and second hydrolysis probes that bind the respective first and second code sites; amplifying the oligonucleotide binders in the droplets in the presence of the first and second probes labeled with a dye and a quencher, wherein the first probe releases a first fluorescent signal upon amplification, and the second probe releases a second fluorescent signal upon amplification, and wherein the first and second fluorescent signal are different; detecting the released first and second fluorescent signal in the droplets to thereby count numbers of the droplets comprising the first or second detectable label; and screening for aneuploidy by determining a statistical difference between the number of droplets comprising the first detectable label and the number of droplets comprising the second detectable label. a 5' region comprising a first universal primer site; a 3' region comprising a second universal primer site; and a central region, wherein the central region of the oligonucleotide binders of the first set comprise target-specific sequences that bind to different regions on a target nucleic acid comprising chromosome 21 and a first code site, and the central region of the oligonucleotide binders of the second set comprise reference specific sequences that bind to different regions on a reference nucleic acid comprising a chromosome other than chromosome 21 and a second code site; exposing the sets of oligonucleotide binders to a sample pool comprising the target nucleic acid and the reference nucleic acid, wherein the first set binds to multiple regions on the target nucleic acid and the second set binds to multiple regions on the reference nucleic acid; removing the unbound oligonucleotide binders; diluting and compartmentalizing the sample in a plurality of droplets at a dilution sufficient that most of the droplets contain no more than a single target or reference nucleic acid bound to binders from the exposing step the droplets further comprising primer species that bind to the universal primer sites and first and second hydrolysis probes that bind the respective first and second code sites; amplifying the oligonucleotide binders in the droplets in the presence of the first and second probes labeled with a dye and a quencher, wherein the first probe releases a first fluorescent signal upon amplification, and the second probe releases a second fluorescent signal upon amplification, and wherein the first and second fluorescent signal are different; detecting the released first and second fluorescent signal in the droplets to thereby count numbers of the droplets comprising the first or second detectable label; and screening for aneuploidy by determining a statistical difference between the number of droplets comprising the first detectable label and the number of droplets comprising the second detectable label.