All the gametes

A cell has a few pairs of homologues. Each gamete gets one chromosome from every pair. You will list all the gametes, and then count the kinds of gamete and of zygote.

The idea. With $n$ pairs, each with 2 choices, there are $2^n$ gametes. Two parents can make $2^n \times 2^n$ zygotes.

Your tasks.

1. Finish gametes. It gives the set of all gametes. A gamete is a tuple with one chromosome from each pair.
2. Finish kinds. It gives the number of kinds of gamete for n pairs.
3. Finish zygotes. It gives the number of kinds of zygote from two parents with n pairs.