I got into a debate with someone in class over an experiment that was claimed to be randomized.
The experiment was such that there is a bucket of distinct objects, and objects were being "randomly" (but independently) selected from the bucket. There are $N$ objects in the bucket, and $M$ random selections are made. The experiment was conducted such that $M>>N$, but $M$ is finite.
It was claimed that this experiment (choosing objects $M$ times) was conducted "randomly," and also that the experiment GUARANTEED that all $N$ objects would be chosen at least once. I think that "randomly" and "GUARANTEED" are mutually exclusive in this instance.
I made the argument that if the experiment guarantees that all $N$ objects would be chosen at least once, then the selections are not conducted randomly. To guarantee that all $N$ objects are selected, with a finite $M$ (albeit being much larger than $N$) would remove the randomness in my opinion? Am I right, or is it possible for this to still be random while guaranteeing all objects are selected at least once?
Note that I am not asking what is the probability of selecting all $N$ samples by making $M$ selections, where $M>>N$. I understand the probability here is close to 1. For the probability to be equal to 1, then $M\rightarrow\infty$.