We want to find the value of $X$ in the given situation.
The probability of drawing the chips in the specified order can be calculated by considering the number of favorable outcomes and the total number of possible outcomes.
The total number of possible outcomes can be calculated by considering the number of ways to arrange the 9 chips, which is given by the factorial of 9 (9!).
The number of favorable outcomes can be calculated by considering the number of ways to arrange the 3 tan chips, 2 pink chips, and $X$ violet chips, which is given by the factorial of (3+2+$X$).
Therefore, the probability can be calculated as:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Given that the probability is $\frac{1}{210}$, we can set up the equation:
$\frac{1}{210} = \frac{(3+2+X)!}{9!}$
Simplifying, we have:
$\frac{1}{210} = \frac{(5+X)!}{9!}$
To solve for $X$, we can cross-multiply and simplify the equation:
$9! = 210 \cdot (5+X)!$
Dividing both sides of the equation by $(5+X)!$, we find:
$210 = \frac{9!}{(5+X)!}$
Given that the value of $X$ is a positive integer, we can try different values and solve for $X$.
Let's start with $X = 1$:
$210 = \frac{9!}{(5+1)!}$
$210 = \frac{9!}{6!}$
$210 = \frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$
$210 = 9 \cdot 8 \cdot 7 = 504$
The equation does not hold true for $X = 1$.
Let's try $X = 2$:
$210 = \frac{9!}{(5+2)!}$
$210 = \frac{9!}{7!}$
$210 = \frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$
$210 = 9 \cdot 8 = 72$
The equation does not hold true for $X = 2$.
Let's try $X = 3$:
$210 = \frac{9!}{(5+3)!}$
$210 = \frac{9!}{8!}$
$210 = \frac{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$
$210 = 9$
The equation does not hold true for $X = 3$.
Let's try $X = 4$:
$210 = \frac{9!}{(5+4)!}$
$210 = \frac{9!}{9!}$
$210 = 1$
The equation holds true for $X = 4$.
Therefore, the value of $X$ is 4.
The answer is: 4
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
A bag contains 3 tan, 2 pink and 4 violet chips. If the 9 chips are randomly drawn from the bag, one at a time and without replacement, what is the probability that the chips are drawn in such a way that the 3 tan chips are drawn consecutively, the 2 pink chips are drawn consecutively, and the X violet chips are drawn consecutively, but not necessarily in the tan-pink-violet order? Express your answer as a common fraction.
If we know the answer to the above question is \frac{1}{210}, what is the value of unknown variable X?

### Answer:
