Out of `3n` consecutive integers, three are selected at random. Find the probability that their sum is divisible by 3.

Explanation

To solve the problem of finding the probability that the sum of three randomly selected integers from `3n` consecutive integers is divisible by 3, we can follow these steps:

### Step 1: Determine Total Ways to Select 3 Integers
The total number of ways to select 3 integers from `3n` integers is given by the combination formula:

\[ \text{Total ways} = \binom{3n}{3} \]
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