Final answer:
The man's genotype is AaRr and the woman's genotype is aaRr. They both can produce AR, Ar, aR, and ar gametes, and the inheritance pattern of their children's traits suggests these genotypes.
Step-by-step explanation:
The probable genotypes of the parents are as follows: The man has freckles and cannot roll his tongue, so his genotype for these traits is likely AaRr, where 'A' represents the allele for freckles and 'a' represents the allele for no freckles, 'R' is the allele for tongue rolling ability, and 'r' is the allele for non-tongue rolling ability.
The woman has no freckles and can roll her tongue, which suggests a genotype of aaRr. The man can produce four different types of gametes: AR, Ar, aR, and ar. The woman can also produce four different types of gametes: aR, ar, aR, and ar.
Since all of their children have freckles, we can deduce that the man must be heterozygous for the freckle trait (Aa) because the children inherit the dominant 'A' allele from him. About half of the children can roll their tongues while the other half can't, which is reflected in the heterozygosity (Rr) of both parents for the tongue-rolling trait.