How do you know the number of gametes produced from a cross?

[Nivea]

I understand that a general formula for
F1 gametes is 2^n,
F2 genotypes is 3^n and
F2 phenotypes would be 2^n,
where n is the number of genes.
However, I am confused how the answers come about, I’m more of a visual learner so I’d benefit more by seeing the different gametes and counting them, math just confuses me.
I was thinking since gametes are haploid then for
a) the potiential gametes would be A and a, which are 2.
Then for b) A,a,B,b which are 4.
And finally c) A,a,B,b,C,c which is 6–but when you do the formula for this one, you get 8? (2^3 = 8 )
I think I am misunderstanding the concept. 🙁 Would someone please explain this, I have a test coming up so I would really appreciate it, thank you so much in advance! 😀

How many different kinds of F1 gametes, F2 genotypes, and F2 phenotypes would be expected from the following crosses:
(a) AA x aa;
(b) AA BB x aa bb;
(c) AA BB CC x aa bb cc?

[JackBean]

You MUST always have all the genes in your gamete, so for two genes you can have AB, Ab, aB or ab; for 3 genes it is ABC, ABc, AbC, aBC, abC, aBc, Abc or abc, that is 8 possibilities 😉

[Nivea]

Ah that makes a lot more sense, thank you! 😀

[Author]

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