Final answer:
The genotype 'bb' is not a possible genotype for polydactyly, as it doesn't represent the correct alleles for the dominant polydactyl trait (P for dominant and p for recessive).
Step-by-step explanation:
The question is about determining which genotype is not possible for your friend who has inherited the polydactyl trait, given it is dominant and neither parent has the trait. Since the trait is dominant (represented by 'P'), the only way for someone to display the polydactyl trait without having parents that show the trait is to have a heterozygous genotype ('Pp'). This is possible if both parents are carriers of the recessive allele ('p') without expressing it themselves, which means they would both be 'Pp'. A genotype of 'PP' would indicate that at least one parent must display the trait, and a genotype of 'pp' would not exhibit the trait at all, since it is recessive. The genotype 'bb' is not relevant to the question, as it does not correspond with the alleles being discussed (P for polydactyl dominant allele, and p for non-polydactyl recessive allele). Therefore, 'bb' is not a possible genotype for polydactyly.