Problem:
12 persons are seated at a circular table. Find the probability that 3 particular persons always seated together.

Solution:
In this problem, we need to find the probability of 3 particular persons always seated together. Let's break down the problem into smaller steps to solve it.

Step 1: Total number of possible arrangements
When 12 persons are seated at a circular table, the total number of possible arrangements is (12-1)! = 11!.

Step 2: Number of arrangements with 3 particular persons seated together
Since the 3 particular persons always need to be seated together, we can consider them as a single entity. So, we have 10 entities (9 remaining persons + 1 entity of 3 persons) to be arranged around the circular table.

The number of arrangements with the 10 entities seated around the circular table is (10-1)! = 9!.

Step 3: Number of arrangements within the group of 3 particular persons
Within the group of 3 particular persons, they can be arranged among themselves in 3! = 6 ways.

Step 4: Calculate the probability
To calculate the probability, we need to divide the number of favorable outcomes (arrangements with 3 particular persons seated together) by the total number of possible outcomes (total number of arrangements).

Number of favorable outcomes = Number of arrangements with 3 particular persons seated together * Number of arrangements within the group of 3 particular persons = 9! * 3!
Total number of possible outcomes = 11!

Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = (9! * 3!) / 11!

Simplifying this expression, we get:
Probability = 3/55

Therefore, the correct answer is option D, 3/55.