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Current estimate of the number of particles existing in the universe:
Somewhere between 10000000000000000000000000000000000000000000000000 00000000000000000000000 (or 10^72) and 10000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000 (or 10^87).
Still, that does not mean that chances of random stuff existing are big in any way. On the contrary, they're almost infinitely small. (basic math: the number of theoretically possible combinations of particles is insanely big, while the number of practically possible combinations is far smaller)
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