Final answer:
In a trihybrid cross between parents heterozygous for all three traits with dominant and recessive patterns, there are 64 different genotypic combinations and 27 different phenotypic combinations of offspring.
Step-by-step explanation:
When looking at a trihybrid cross, we are examining the inheritance of three separate traits. If each trait is governed by a gene with two alleles having a dominant and recessive pattern, we can analyze the potential outcomes. In a trihybrid cross, such as the one between parents heterozygous for all three traits, we must consider the independent assortment of each allele and the dominant-recessive interaction.
The number of phenotypic combinations can be determined by considering each trait separately. For example, with the classic Mendelian 3:1 ratio for dominant to recessive traits, the phenotypic pattern for each trait would imply that three quarters of the offspring would show the dominant phenotype for that trait, and one quarter would show the recessive phenotype.
Applying the forked-line method, we find that the number of phenotypic combinations is the product of the ratios for each trait. In this case, it would be 3 (dominant-dominant) x 3 (dominant-dominant) x 3 (dominant-dominant) for the dominant phenotype of all three traits, producing 27 different phenotypic combinations from a trihybrid cross.
Furthermore, considering all the combinations, there would be a total of 64 different genotypic combinations (4 x 4 x 4 = 64), as each gene can have two alleles, and there are three genes each capable of combining in a 4x4 Punnett square. So the correct answer to the possibility of different genetic and phenotypic combinations of offspring from a trihybrid cross would be 64 genotypes and 27 phenotypes.