Suppose a genotype for a protein-producing gene can have any combination of three alleles, A₁, A₂, and A₃.
List all the possible genotypes involving these three alleles.

Verified step by step guidance

1. Understand that the problem involves three alleles (A₁, A₂, A₃) and that genotypes are combinations of two alleles because diploid organisms have two copies of each gene.
2. Recognize that the combinations can include both homozygous genotypes (where the two alleles are the same, e.g., A₁A₁) and heterozygous genotypes (where the two alleles are different, e.g., A₁A₂).
3. List all possible homozygous genotypes: A₁A₁, A₂A₂, and A₃A₃.
4. List all possible heterozygous genotypes by pairing each allele with the others without repetition: A₁A₂, A₁A₃, and A₂A₃. Note that the order of alleles does not matter (e.g., A₁A₂ is the same as A₂A₁).
5. Combine the homozygous and heterozygous genotypes into a complete list: A₁A₁, A₂A₂, A₃A₃, A₁A₂, A₁A₃, and A₂A₃.

Key Concepts

Alleles

Alleles are different versions of a gene that can exist at a specific locus on a chromosome. In this case, the alleles A₁, A₂, and A₃ represent variations of a gene responsible for producing a particular protein. Each individual inherits two alleles for each gene, one from each parent, which can be the same (homozygous) or different (heterozygous).

Genotype

A genotype refers to the specific genetic makeup of an individual concerning a particular gene or set of genes. It is represented by the combination of alleles present, such as A₁A₁, A₁A₂, or A₂A₃. Understanding genotypes is crucial for predicting phenotypic traits and inheritance patterns in offspring.

Combinatorial Genetics

Combinatorial genetics involves calculating all possible combinations of alleles to determine potential genotypes. With three alleles (A₁, A₂, A₃), the possible genotypes can include homozygous combinations (e.g., A₁A₁) and heterozygous combinations (e.g., A₁A₂, A₁A₃, A₂A₃). This concept is essential for understanding genetic variation and inheritance.