Final answer:
In genetics, a diploid organism can have a total of 21 different possible genotypes for a gene with six possible alleles, considering both homozygous and heterozygous combinations.
Step-by-step explanation:
For a gene with six possible alleles, there are 21 different possible genotypes. To determine this, we use the combination formula for choosing 2 out of 6, which is expressed as 6! / (2!(6-2)!) = 15. However, this calculation only accounts for heterozygous combinations. Since there are also 6 homozygous combinations (each allele paired with itself), we must add these to our total, yielding 15 + 6 = 21.
Understanding the concept of multiple alleles extends beyond Mendel's two-allele model. In diploid organisms, such as humans, an individual can carry two alleles (variants) for a given gene. Even though an individual can only possess two of these alleles, a larger set may exist within a population, making the calculation of potential genotypes more complex. The combination of two alleles an organism possesses comprises its genotype, which can be either homozygous (the same two alleles) or heterozygous (two different alleles).
As a didactic note, this problem illustrates the mathematical application in biological context, specifically in genetics, where the distinction between phenotype (observable traits) and genotype (genetic makeup) is crucial for inheritance patterns.