Which setup could not be used to induce an electric current?
spinning wire coils within an array of fixed permanent magnets
spinning electromagnets within an array of fixed wire coils
spinning permanent magnets within an array of fixed permanent magnets
spinning wire coils within an array of fixed electromagnets

Spinning permanent magnets within an array of fixed permanent magnets.

Explanation:

Any relative motion between magnets (be they permanent or electromagnetic) and a coil of wire will induce an electric current in the coil.

What will not induce an electric current is the relative motion between the two coils of wire (because there is no change in magnetic field), or the relative motion between two magnets (there are no coils of wire to induce the current into).

Therefore, spinning permanent magnets within an array of fixed permanent magnets does not induce an electric current.  

In all other choices,  coils of wire are there to be induced current into, and magnets are present to create changing magnetic fields.