The example that would likely result in new combinations of DNA in an individual's offspring is:
Homologous chromosomes failing to separate during meiosis.
This event, known as nondisjunction, can result in gametes with an abnormal number of chromosomes, leading to genetic variation in the offspring once fertilization occurs. The other options involve mutations or cellular processes that do not contribute to genetic variation in offspring since they pertain to somatic (non-reproductive) cells or processes not related to the formation of gametes.