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The number of possible combinations of genes is so large that the chance of a random duplication is vanishingly small. Even twins aren't exact copies because they'll have mutations unique to themselves.
The question isn't whether it's large. The question is how large is it? Right now the human population doubles every 40 years and that rate seems to be increasing.
If humans somehow expanded in population and efficiently consumed all of the energy in the universe, then that means maybe somewhere on the order of 10^65 possible people (according to some very bad napkin math just for the sake of argument).
Are there that many unique combinations of human DNA, ignoring mutations which would change the species or have no impact on biology?