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There are only two real answers, either 0 or 1.
If you are going topologically the answer is one, just like a donut.
Personally I like to think of a straw as a hollow cylinder of plastic, in which case the "hole" in the center is just space the cylinder doesn't occupy and not actually a hole, so zero.
Two holes doesn't even make any sense imo.
Try punching 2 holes in your tire, and demand to pay for at most 1 puncture repair, let's see how far that 0 or 1 hole argument gets you :)
By that logic a tire has 0 holes in it by default, so a straw should have 0 holes as well :)