If the random variables $X_1,...,X_n$ are I.I.d. when conditioned on an unknown parameter $\theta$, where $p(\theta)$ represents our prior beliefs about $\theta$, it follows from the commutativity of the product that $X_1,...,X_n$ are exchangeable.
In my professor's lecture notes, he goes on to write that because $X_1,...X_n$ are exchangeable, it holds that $X_1,...X_n$ are dependent. I'm having a hard time understanding why this is the case.
What if I rolled a dice three times? Then the outcomes are exchangeable, I.e. $P[(4,5,6)]=P[(5,4,6)]=P[(6,4,5)]$, yet the three rolls are independent. Am I missing something?