Cross problem

[sims262]

Can anyone help me with this problem?

A female of genotype AaBBCCDD is mated to a male of genotype aaBBCcdd. What are the expected genotypic proportions of the offspring (assuming no linkage)?

I'm guessing there is some sort of equation or relationship to the number of heterozygous alleles at each loci, but I can't figure it out. Thanks!

[vienna]

Parents: Female x Male
Genotype: AaBBCCDD x aaBBCcdd
Gametes formed: A, a, B, C, D a, B, C, c, D
Hence combining the different types of gametes one can find the genotypes that can be produced by the given combination of parental genotypes.]
Genotypes of offsprings: AaBBCCDD, aaBBCCDD, AaBBCcDD and aaBBCcDD.
This can be formulated as follows:
Number of genotypes formed = 2^Number of characteristics that are heterozygous.
In this case only 2 characterisics are heterozygous hence the types of gametes formed will be 2 x 2 = 4.

[sims262]

That's all well and good, but doesn't really answer the question. I still need to know in what proportions those possible phenotypes occur.