A freshman can calculate that the probability of picking $k$ blue balls after sampling $n$ balls from a bin of $K$ blue balls and $N-K$ red balls is $$\frac{\dbinom{n}{k} \dbinom{N-n}{K-k}}{\dbinom{N}{K}}$$ if one samples without replacement, while it is $$\frac{\dbinom{n}{k} (\frac{K}{N})^k(\frac{N-K}{N})^{n-k}$$ if one samples with replacement. We demonstrate that comparing probabilities of sampling with replacement vs. without replacement leads to De Finetti's Theorem, the Aldous-Hoover Theorem, and even a weak form of Szemeredi's Regularity Lemma which plays a crucial role in the study of graphons. This comparison also leads to a strong version of a representation for DAG-exchangeable arrays (Jung, Lee, Staton, Yang (2021)) which generalize Aldous-Hoover arrays as well as Hierarchical Exchangeable arrays (Austin-Panchenko (2014)).