Crossing over and random alignment are the events of meiosis-I that add new gene combinations to the gametes. Random fusion of male and female gametes is called random fertilization.
Explanation:
During the pachytene stage of meiosis-I, part of the chromatids of each of the homologous chromosomes of a bivalent is broken apart and exchanged. This exchange of the genetic material between the members of a bivalent is called crossing over. The recombinant chromatids formed by crossing over have new allele combinations that were otherwise not present in the parental chromatids.
During metaphase I, the homologous pairs are aligned at the cell's equator in a random manner. This means that either the paternal or maternal chromosome of a pair may face one or the other pole of the cell. The arrangement of chromosomes during metaphase-I determines whether the paternal or maternal chromosome of each pair would be distributed to one or the other pole of the cell. This random segregation creates new gene combinations in gametes.
All the gametes have equal chances of getting fused with a gamete from the opposite gender. This is called random fertilization and further adds variations.
