In sexually reproducing organisms, chromosomes occur in pairs, one member from the mother and one from the father. During gamete formation (meiosis), the two members of each pair separate, and which one goes into a particular gamete is decided independently and randomly for every pair. This independent assortment shuffles maternal and paternal chromosomes into countless new combinations, and that is the main source of variation in the offspring.

Frequent cell divisions by themselves simply make more cells and do not create new combinations of genes. A change in chromosome number is usually an error that leads to abnormalities, not the normal way diversity is generated. Copying errors in DNA do introduce mutations, but these are relatively rare and are not the primary mechanism; the major, routine source of diversity in sexual reproduction is the random reassortment of whole chromosomes.

Hence, the answer is the random distribution of maternal or paternal chromosomes from each chromosome pair to the gametes.