Suppose I prepare following state consisting of (for example) three EPR pairs:
$$\lvert\Psi\rangle = \frac{\lvert00\rangle+\lvert11\rangle}{\sqrt{2}}\otimes\frac{\lvert00\rangle+\lvert11\rangle}{\sqrt{2}}\otimes\frac{\lvert00\rangle+\lvert11\rangle}{\sqrt{2}}$$
Then I shuffle the second qubits of all pairs before giving you the full (shuffled) state. You would not know which pairs of qubits form EPR pairs. Does this mean you would have a mixed stated over all possible permutations? How can I write such state?