# Confused with gamete sorting problem

A man has the genotype AaBbCc, in other words he is heterozygous in three uncoupled loci on three different chromosomes. A, B and C are the dominant alleles while a, b and c are the recessive alleles.

1. How many gametes can he form?

The answer is 8 and I can see how you derive that by just manually writing each and every one down but what is the mathematical method to derive this? I tried permutations but none I came up with worked.

2. He has a child with a woman of the same genotype (AaBbCc) how many different genotypes can the offspring have?

Here the answer is 27. I'm not sure how they came to this conclusion either?

3. What is the probability that the offspring has the genotype AaBbCc?

This is about the time I start flipping tables because it seems to me that it's 1 out of 27. There are 27 different genotypes and this is ONE of them?!

But the answer is 1/8 as there's a 50% chance of Aa, Bb and Cc when mixing apparently so it becomes 1/2*1/2*1/2. Why isn't it just 1 of the possible genotypes? 