Problem 2.157

A vessel of volume $V_{0}$ contains $N$ molecules of an ideal gas. Find the probability of $n$ molecules getting into a certain separated part of the vessel of volume $V$ . Examine, in particular, the case $V=V_{0} / 2$

P_{n}=\frac{N !}{n !(N-n) !} p^{n}(1-p)^{N-n}, \text { where } p=V / V_{0}

Second law of thermodynamics, entropy