In order to define temperature in terms of statistics, "Concepts of Thermal Physics" by Blundell states:
Let us assume that the first system can be in any one of $Ω_1(E_1)$ microstates and the second system can be in any one of $Ω_2(E_2)$ microstates. Thus the whole system can be in any one of $Ω_1(E_1)Ω_2(E_2)$ microstates.
as expected from the probabilities.
However, when is considered that when the two systems can exchange energy with each other, it is stated that:
For our problem of two connected systems, the most probable division of energy between the two systems is the one which maximizes $Ω_1(E_1)Ω_2(E_2)$, because this will correspond to the greatest number of possible microstates.
My question is: Given the fact that occurs an exchange of energy between the two systems, I was expected that we will have:
$\Omega_{1+2} \geq \Omega_{1}\Omega_{2}$ as the number of microstates for the whole system
Could anyone explain me what is wrong above in my argument?´