To determine the number of plants with the genotype AabbCc out of 256 seeds collected from F2 progenies of a trihybrid cross, we need to understand the principles of Mendelian genetics and the inheritance patterns associated with the genes involved.



Mendelian genetics is the study of how traits are passed from one generation to the next. Gregor Mendel, the father of modern genetics, discovered that traits are controlled by discrete units called genes, which are located on chromosomes.

Inheritance patterns can be classified into different types, such as dominant/recessive, codominant, and incomplete dominance. In this case, we need to consider the dominant/recessive inheritance pattern.



A trihybrid cross involves the crossing of individuals that differ in three traits. In this case, we are interested in the genotype AabbCc, which means that the individual has the dominant allele (A) for the first trait, the recessive allele (b) for the second trait, and the dominant allele (C) for the third trait.

When performing a trihybrid cross, we can use a Punnett square to determine the potential genotypes and phenotypes of the offspring. However, since we are only interested in the genotype AabbCc, we need to consider the specific combination of alleles that results in this genotype.



To obtain the genotype AabbCc, we need to consider the specific combination of alleles for each trait. Let's assume that each trait is controlled by a single gene with two alleles, where A is dominant and a is recessive, and C is dominant and c is recessive.

The genotype AabbCc can be obtained from the following combinations:

- First trait (A or a): Aa or aa (2 possibilities)
- Second trait (B or b): bb (1 possibility)
- Third trait (C or c): Cc (1 possibility)

Therefore, the total number of possible genotypes that can produce AabbCc offspring is 2 (Aa or aa) x 1 (bb) x 1 (Cc) = 2.



Since we collected 256 seeds from the F2 progenies, we can expect that approximately 1/4 of the seeds will have the genotype AabbCc.

Therefore, the number of plants produced with the genotype AabbCc would be approximately 256 / 4 = 64 plants.

It's important to note that these calculations are based on Mendelian genetics and assume independent assortment of genes, which may not always be the case in real-life situations due to factors such as gene linkage and genetic interactions.