I'm preparing my statistical physics course, and while writing the lecture notes it says that a system with non distinguishable particles has much less microstates asociated with a particular macrostate. Hence, a system with distinguishable particles has much more microstates asociated with a particular microstate. Entropy $S$ is related with the number of microstates $\Omega$ via:
$$S=k \ln (\Omega) $$
where $k$ is Boltzmann's constant. Then my question is
Given the same macrostate for both systems, the entropy of the first is much lower than the entropy of the second?
Thanks for your time.