I have a system consisting of N distinguishable particles. Each particle has two states, one with energy E and the other with energy 0. The number of particles in the state with energy 0 is $n\_{0}$ and the number of particles in the second state is $n\_{1}$. The number of particles in the different states satisfy $N=n\_{0}+n\_{1}$. 
Now I want to compute the number of available microstates in the microcanonical ensemble that are in agreement with the energy constraint $U=n\_{1}\*E$.

Since the particles are distinguishable I can arrange them in $N!$ ways. And since I have two states the total number of possibilities to arrange this system is $2\*N!=2\*(n\_{0}+n\_{1})$. Hence the partition function is:

$$
\Omega(U,N)=2\*(n\_{0}+n\_{1})!
$$

Now I want to compute the entropy in the microcanonical ensemble and maximize it with respect to U. 
I guess the maximum will be at $n\_{0}=n\_{1}=N/2$
But I don't know how to show this. My feeling somehow tells me I should use Lagrange multipliers and maximize $\Omega$.