Pedantically, it would have to be finite, because there is a size limit. Cancer couldn't transform your genome into a piece of DNA the size of the sun.
It's not because it's finite that the number of combinations possible is limited. Just like for passwords, the more bits involved, the more possibilities you get, and a DNA or RNA is a molecular version of a very, very long password. So "finite" is a very poor way to describe the complexity.
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Pedantically, it would have to be finite, because there is a size limit. Cancer couldn't transform your genome into a piece of DNA the size of the sun.
Just to out-pedant you, the size of the sun is still quite finite, most (all?) things are.
Perhaps colloquially, finite here is (not un-like literally) a metaphor, in this case for not-unfathomably-large, or more precisely, measurable.
It's not because it's finite that the number of combinations possible is limited. Just like for passwords, the more bits involved, the more possibilities you get, and a DNA or RNA is a molecular version of a very, very long password. So "finite" is a very poor way to describe the complexity.