Sources of genetic variation
Crossing over exchanges corresponding DNA segments between nonsister chromatids of paired homologs during prophase I. Different homolog pairs orient independently at metaphase I, producing different combinations of maternally and paternally inherited chromosomes. Even without crossing over, n chromosome pairs can generate 2^n chromosome combinations through independent assortment. Random union of gametes adds further combinations. Recombination changes combinations; it does not intentionally generate alleles that an organism needs.
An organism with n = 4 has 16 possible whole-chromosome combinations in gametes from independent assortment alone; crossing over increases the possible sequence combinations.
Independent assortment describes how different homolog pairs orient, not sister chromatids randomly forgetting where to go.