A method of testing for the presence or absence of a fetal aneuploidy in a maternal plasma sample comprising a mixture of maternal and fetal cell-free DNA, comprising the steps of: (a) obtaining a mixture of maternal and fetal cell-free DNA from said sample; (b) sequencing predefined subsequences of the maternal and fetal cell-free DNA, to obtain a plurality of sequence tags aligning to the predefined subsequences, wherein the sequencing comprises selectively sequencing nucleic acid molecules comprising the predefined subsequences using a sequencing method which selectively captures sample molecules containing the predefined subsequences, wherein said sequence tags are of sufficient length to be assigned to a specific predefined subsequence, wherein the predefined subsequences are from a plurality of different chromosomes, and wherein said plurality of different chromosomes comprise at least one first chromosome suspected of having an abnormal distribution in said sample and at least one second chromosome presumed to be normally distributed in said sample, wherein the selective capture is directed to predefined subsequences mapping uniquely or with one mismatch to said at least one first chromosome and said at least one second chromosome, and wherein said at least one first chromosome is chromosome 18, 21, 13, X or Y; (c) assigning the plurality of sequence tags to their corresponding predetermined subsequences; (d) determining a number of sequence tags aligning to the predetermined subsequences of said first chromosome and a number of sequence tags aligning to the predetermined subsequences of said second chromosome; and (e) using the numbers from step (d) to determine a differential, between the number of sequence tags aligning to the predetermined subsequences of said first chromosome and the number of sequence tags aligning to the predetermined subsequences of said second chromosome, which is determinative of the over-representation or under-representation of said first chromosome in the mixture of maternal and fetal cell-free DNA. (a) obtaining a mixture of maternal and fetal cell-free DNA from said sample; (b) sequencing predefined subsequences of the maternal and fetal cell-free DNA, to obtain a plurality of sequence tags aligning to the predefined subsequences, wherein the sequencing comprises selectively sequencing nucleic acid molecules comprising the predefined subsequences using a sequencing method which selectively captures sample molecules containing the predefined subsequences, wherein said sequence tags are of sufficient length to be assigned to a specific predefined subsequence, wherein the predefined subsequences are from a plurality of different chromosomes, and wherein said plurality of different chromosomes comprise at least one first chromosome suspected of having an abnormal distribution in said sample and at least one second chromosome presumed to be normally distributed in said sample, wherein the selective capture is directed to predefined subsequences mapping uniquely or with one mismatch to said at least one first chromosome and said at least one second chromosome, and wherein said at least one first chromosome is chromosome 18, 21, 13, X or Y; (c) assigning the plurality of sequence tags to their corresponding predetermined subsequences; (d) determining a number of sequence tags aligning to the predetermined subsequences of said first chromosome and a number of sequence tags aligning to the predetermined subsequences of said second chromosome; and (e) using the numbers from step (d) to determine a differential, between the number of sequence tags aligning to the predetermined subsequences of said first chromosome and the number of sequence tags aligning to the predetermined subsequences of said second chromosome, which is determinative of the over-representation or under-representation of said first chromosome in the mixture of maternal and fetal cell-free DNA.