To find the probability that all three balls drawn are of the same color, we need to calculate the favorable outcomes and divide it by the total number of possible outcomes.

**Step 1: Find the favorable outcomes**
There are three possible outcomes where all three balls are of the same color: either all red, all white, or all blue.

- Possible outcome 1: All red balls
The probability of drawing the first red ball is 6/18 (since there are 6 red balls out of a total of 18 balls).
After drawing the first red ball, there are 5 red balls left out of 17 balls.
So the probability of drawing the second red ball is 5/17.
Similarly, the probability of drawing the third red ball is 4/16.
Therefore, the probability of drawing all three red balls is (6/18) * (5/17) * (4/16).

- Possible outcome 2: All white balls
The probability of drawing the first white ball is 4/18 (since there are 4 white balls out of a total of 18 balls).
After drawing the first white ball, there are 3 white balls left out of 17 balls.
So the probability of drawing the second white ball is 3/17.
Similarly, the probability of drawing the third white ball is 2/16.
Therefore, the probability of drawing all three white balls is (4/18) * (3/17) * (2/16).

- Possible outcome 3: All blue balls
The probability of drawing the first blue ball is 8/18 (since there are 8 blue balls out of a total of 18 balls).
After drawing the first blue ball, there are 7 blue balls left out of 17 balls.
So the probability of drawing the second blue ball is 7/17.
Similarly, the probability of drawing the third blue ball is 6/16.
Therefore, the probability of drawing all three blue balls is (8/18) * (7/17) * (6/16).

**Step 2: Find the total number of possible outcomes**
To find the total number of possible outcomes, we need to calculate the number of ways to choose 3 balls out of 18 balls, which can be done using the combination formula:
C(n, r) = n! / (r! * (n-r)!)
where n is the total number of balls and r is the number of balls drawn.

Using this formula, the total number of possible outcomes is:
C(18, 3) = 18! / (3! * (18-3)!) = 18! / (3! * 15!) = (18 * 17 * 16) / (3 * 2) = 816

**Step 3: Calculate the probability**
The probability of all three balls being of the same color is the sum of the probabilities of the three possible outcomes (all red, all white, all blue), divided by the total number of possible outcomes:
Probability = (favorable outcomes) / (total outcomes)
Probability = [(6/18) * (5/17) * (4/16)] + [(4/18) * (3/17) * (2/16)] + [(8/18) * (7/17) * (6/16)] / 816

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