Two distinguishable particles in a box.

[peripatein]

Hi,

Homework Statement

I would like to determine the number of energy states two free, distinguishable particles in a box of length L have. I would then like to determine the number of states two free, indistinguishable particles, with spin 3/2 each, have in that box at the elementary level. Finally, determine the number of states in case these two particles with spin 3/2 each are distinguishable.

Homework Equations

The Attempt at a Solution

I am familiar with the following formula for the energy states
E_n=(hbar)²π²n²/(2mL²)
but am not sure how to proceed. If the particles are distinguishable, does that entail that one is a fermion whereas the other is a boson? I am not sure.
Furthermore, if the two particles have spin 3/2 each, that means they are both fermions, right? If that is correct, then, due to Pauli's exclusion principle, the two could not be at the same state. I also know that for spin 3/2 there could be 4 particles per energy level. But again I am not sure how to coherently process the given data and would appreciate some guidance.

 

[peripatein]

In case the spin of each particle is 3/2, would the number of energy states be 4!/(2!2!) for indistinguishable particles and 4!2! for distinguishable particles? (at the elementary level)