How Does the Multiplicity of a Classical Gas Relate to Ideal Gas Conditions?

[S_Flaherty]

Homework Statement

Consider the multiplicity of a classical gas of N non-interacting molecules (not necessarily monatomic). Since they don't interact,their positions are not correlated, so the multiplicity of each will be simply proportional to the volume, with the result that the total multiplicity Ω = V^Nf_N(U), where f_N is some function of the total internal energy. Show that this implies the two conditions for an ideal gas.

Homework Equations

Ω(N,n) = N!/[n!(N-n)!]
PV = NkT

The Attempt at a Solution

I'm not really certain how to go about this. Would the two conditions be referring to the ideal gas law PV = NkT = nRT and that a entropy and multiplicity increase?

 

[S_Flaherty]

Can anyone tell me if I'm on the right track so far?