Final answer:
Using Mendel's Law of Independent Assortment, an organism with three chromosome pairs can produce eight genetically different sex cells, calculated by the formula 2^n, where n is the number of chromosome pairs.
Step-by-step explanation:
Imagine an organism with three chromosome pairs. According to Mendel's Law of Independent Assortment, we can calculate the number of genetically different sex cells this organism could produce. Mendel's law suggests that alleles of different genes assort independently of one another during gamete formation. The formula to calculate the number of different gametes is 2n, where n represents the number of chromosome pairs.
For an organism with three chromosome pairs (n = 3), we would calculate 23, which equals 8. Therefore, this organism could produce eight genetically different sex cells, assuming no crossing over occurs. This variation is due to the different ways in which the chromosomes can independently assort during metaphase I of meiosis, leading to a variety of combinations in the resulting gametes.