It depends on how many SNPs (read as 'snip') they map and how much variation is at each site. It basically boils down to a combinatorial counting problem, although there is the complication that variation across close SNPs might not be independent (especially if they are on the same gene, or are related in some phenotypic way).

This is also the basis for DNA forensics/paternity tests. If you sample enough SNP locations you should theoretically have a unique signature (this is where you get the courtroom statistic of 1 in 3 million)