Consider two systems A and B in thermal contact. System A has $N_A=3$ simple harmonic oscillators and the system B has $N_B=3$ simple harmonic oscillators as well. Each system has a number of energy units $q$ (macrostates of the statistical system) such that $q=q_A+q_B=6$.
By applying the formula for the multiplicity of the systems, $$\Omega(N,q)=\frac{(q+(N-1))!}{q! (N-1)!}$$ and the fact that the total number of multiplicities is given by $\Omega_{total}=\Omega_A\Omega_B$ we obtain the following combinations of energy units {$q_A,q_B$}:
{0,6} = 28,
{1,5} = 63,
{2,4} = 90,
{3,3} = 100,
{4,2} = 90,
{5,1} = 63,
{6,0} = 28.
As far as my understanding goes, this then implies that the most likely outcome for the interacting systems is each having 3 energy units. However, the fundamental assumption of statistical physics states the following:
In an isolated system in thermal equilibrium, all accessible microstates are equally probable.
Surely this would then imply that {0,6} is no less likely to occur than {3,3}, since all accessible microstates are equally probable, thereby making q=0 and q=6 just as likely to occur as q=3 and q=3.
Can someone please explain to me where my misunderstanding lies?