From a mathematical point of view, if there are 20,000 genes in the human genome, how do we calculate the number of possible humans that can statistically be produced (without mutation)?

eg. Does each gene correspond to one of A,C,G,T? In which case an upper limit would be 4^20000? Or is this totally wrong? I'm thinking in terms of very rough figures.

Maybe another approach to the question is in terms of DNA sequencing... if someone looks at my DNA, what chance is there that someone else will have the same result? Or that I have the same DNA as someone else?

Obviously some combinations will not work, but am I right in thinking that if any 2 of the 7 billion humans have a child, that there are real and quantifiable boundaries to the human genome that say, without mutation, that "there is a possibility of producing this offspring" with certain DNA, but you're never going to produce an ape- that is too far different from a human.

So there must be a finite number of genetically distinct humans that can be made from combinations of the present human genome... but how can this number be calculated?

Sorry for the ramble, any help much appreciated.