Computational methods were employed to determine progression inference of genomic alterations in commonly occurring cancers. Using cross-sectional TCGA data, we computed evolutionary trajectories involving selectivity relationships among pairs of gene-specific genomic alterations such as somatic mutations, deletions, amplifications, downregulation, and upregulation among the top 20 driver genes associated with each cancer. Results indicate that the majority of hierarchies involved TP53, PIK3CA, ERBB2, APC, KRAS, EGFR, IDH1, VHL, etc. Research into the order and accumulation of genomic alterations among cancer driver genes will ever-increase as the costs of nextgen sequencing subside, and personalized/precision medicine incorporates whole-genome scans into the diagnosis and treatment of cancer.