We're calculating the result of a 'tweaked' Birthday Problem, but when we're calculating, we stumped by a very nasty permutation.
$$10^{576}P_{10^{16}}$$
Which, make us stop working at the number, and call the day.
The formula of the permutation that we understand is:
$$\frac{10^{576}!}{10^{16}!}$$
Is there anyway how do at least 'predict' the length of the number? We already give up on knowing the result, so we just wonder of the massiveness of the number.
The number of digits would be about $575* 10^{576}$. The $10^{16}$ wouldn't even make a dent in that.
On the other hand, I think $10^{576}P_{10^{16}}$ is the product of $10^{16}$ numbers, all very close to $10^{576}$. That would be $$(10^{576})^{10^{16}}$$ which has $5760000000000000000$ digits.