Basic Probability Question

Hi, I'm analyzing how valid a solution is to a problem, and I've realized that it's correctness can't be guaranteed. I've translated it into a math problem to try and figure out how correct of a solution it is. But it's been a while since I've done any math, I was hoping someone could help me out.

MATH VERSION:

If there are a pool of 24 unique numbers

and I pull one at random and write it down if I haven't seen it before

then place it back in

and I do this 1000 times in total

how likely is it that I will have written down 24 numbers?

REAL VERSION:

A one line permutation generator receives an array with 4 functions, sorts them into a random order 1000 times, then keeps the unique sortings. I've ran it probably 10_000 times and always gotten the same results, and am debating whether I should keep trying to get it to fail.