Final answer:
In a one gene/three allele system with co-dominance, there are six different possible genotypes. In this case, the allelic pairs can be AA, AB, AC, BB, BC, and CC since each allele shows co-dominance with the other.
Step-by-step explanation:
In a one gene/three allele system that displays co-dominance with each other, you can determine the number of different genotypes by using the combination formula for pairs from the three different alleles. In this case, the allelic pairs can be AA, AB, AC, BB, BC, and CC since each allele shows co-dominance with the other and you can also have combinations of the same alleles such as AA, BB, and CC. Therefore, there are a total of six different genotypes possible for a one gene/three allele system showing co-dominance.