A vessel of volume `V_0` contains `N` molecule of an ideal gas. Find the probability of `n` molecules getting into a certain separated part of the vessel of volume `V`. Examine, in particle, the case `V = V_0//2`.

Explanation

To find the probability of `n` molecules getting into a certain separated part of the vessel of volume `V`, we can use the principles of combinatorics and probability. Here's a step-by-step solution:

### Step 1: Define the Problem
We have a vessel of total volume \( V_0 \) containing \( N \) molecules of an ideal gas. We want to find the probability that exactly \( n \) molecules are in a smaller volume \( V \).

### Step 2: Calculate the Probability of One Molecule
The probability \( P \) that a single molecule is found in the volume \( V \) is given by the ratio of the volumes:
\[
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