I believe that all those problems could be solved with a Punnet square approach.
I have never used the formulae you mentioned but they would fall out of using a good understanding of making Punnet squares.
a) is correct. The reason is that you are determining the number of different gametes possible. It is done by figuring out how many different possible gene alleles (haploid, one allele from each gene or locus) you can get from each locus and multiplying those numbers together to get the total of genetically different possible gametes.
Writing all the possible gametes from each parent will populate the the two axes (or outer edges) of the Punnet square (one being male, the other female), each axis being having all the possibilities. In the example a, you have five genes where there are two possibilities and one with only one, so you would get 2 x 2 x 2 x 2 x 2 x 1 = 32 or 2
6 as you formula says.
Here is an unrelated example of a Punnet square:
Since you are doing so many different combinations, doing a Punnet square by hand may not be so simple, but knowing how it is assembled will let you walk through the different combinations, multiply things out and get the same answer.
b) From a Punnet square point of view, you want to determine the number of possible different combinations of that could be produced from the two sets of gametes that you got in a.
This is a little more complicated.
Since each gene potentially has one of two alleles and you are considering genotypes (the underlying genetics) of the progeny, so you have a maximum of three possible genotypes. however, you have to look at each possible set of gametes from the two parents because it is possible to only get one, two or three different combinations depending on the gametes being produced by the parents.
Figure out the number of possible genotypes for each locus and multiple them together.
(All of the multiplying together is based on the different loci sorting out separately.)
The formula 3
n would only work for the cases were there are three possible genotypes at n different loci.
If there were loci with two or one possible genotypes that would have to be used when multiplying together the numbers for each loci instead.
c) concerns how many different phenotypes would arise in the progeny. The phenotypes result from the genotypes found in b.
The maximum number of phenotypes will be two and the minimum will be one for each locus.
All the genes have either dominant or recessive alleles, so you will get all recessive genotypes only when you have only recessive genotypes in the cross. In all other cases you will have some dominant alleles which will give the dominant phenotype. If only one parent has the recessive allele for a locus, you will get 0 recessive phenotypes (because they are recessive and require getting a recessive allele from each parent).
Multiple the number you get for each locus together to get your total.
d) Yes, as I described. However, the Punnet square provides a nice (for me) visual way to thing about how to come up with the numbers.
e) Assume the possibility of getting each different allele of a gene as 50% (or 0.5).
Run through you parentals and determine the probability of getting the different possible genotypes necessary for producing the phenotypes corresponding to each gene.
I would think of it as a simple Punnet square for each individual gene.
Multiple together the probabilities for each individual gene together to get total probably for the complex situation they are asking you about.
As I said, I am unfamiliar with the formulae you are using, but there are many different ways to figure these things out.
They should all produce the same result if they are valid.
Better then just trying to follow formulae is to understand why the formulae are used and even better, being able to reproduce the formula from your understanding of how things work.
The Punnet square is a visual approach that works well for me in this way.
This is a complex problem. Hopefully I don't have any goofs in it, but it is possible, so you should check which I say with your own logic.
