= Sampling without replacement need not be independent
Draw two different labels uniformly from $\{1,2,3,4\}$ using <sampling without replacement>. Each position has a <uniform distribution on a finite set>, but $\mathbb P(X_1=X_2)=0$. Two <independent random variables> with those same <marginal distributions> would match with probability $1/4$. Equal marginal laws therefore do not make this sample an <IID sample>. Mark some of those four labels as successes. Their count in the two draws has a <hypergeometric distribution>; independent <Bernoulli trials> with a common success probability give a <binomial distribution>.
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