Final answer:
In a cell with 3 pairs of homologous chromosomes, there would be 2^3 or 8 unique configurations of chromatids in gametes due to random orientation in metaphase I.
Step-by-step explanation:
If a cell has 3 pairs of homologous chromosomes, the number of unique configurations of chromatids in gametes as a result of random orientation during metaphase I can be determined by the formula 2n, where n is the number of chromosome pairs. Thus, for 3 pairs of chromosomes, the number of unique configurations would be 23 or 8 different combinations.
This random orientation is a key factor in generating genetic diversity through independent assortment, which, along with crossover in prophase I, ensures that gametes are genetically unique. Considering humans with 23 pairs of chromosomes, this leads to more than eight million possible combinations, not including variations introduced by crossover. However, for this specific scenario with n = 3, we strictly focus on the chromatid configurations that result from the random orientation during metaphase I.