Example of a system where we can't measure the total possible microstates of a system but can measure the microstates of most probable state? I have been reading about entropy and I read that entropy is basically a measure of total possible microstates but there was an approximation that when no. of particles become very large we take microstates corresponding to most possible macrostate.
Why is this approximation required?
Are there cases where finding the total no. of microstates is not practically possible?
 A: For most systems we can't measure either and nature doesn't really care about putting systems trough all of their microstates or having it anywhere close to the most likely macrostate. Equilibrium is just as much a hypothetical concept as the ergodic hypothesis. Equilibrium is limited by how well a system can be isolated from external energy sources or thermal baths at different temperatures and a physical implementation of ergodicity would require the observation of a system for timescales that are many times longer than the total duration of the current universe, even for relatively small systems. Obviously both can only be approximated both by physicists and nature outside of the lab.   
As with anything other that turns out to be useful in physics, the limits nature sets on how well our theoretically ideal situations are implemented impacts the usefulness of thermodynamics and statistical mechanics relatively little. Like all other physical approximations they are judged by their relative correctness when compared to experimental data (post-hoc) and thermodynamics is "good enough" under fluctuations and in near equilibrium and statistical mechanics works without full ergodicity. We acknowledge the latter when we use carefully selected subsets of microstates in e.g. molecular dynamics simulations (as averaging over all possible microstates is typically impossible with available computing resources). 
