The binomial coefficient $\binom{n}{k}$ represents the number of ways to choose $k$ items from a set of $n$ items, without regard to order.
In this case, we want to choose 9 items from a set of 11 items.
The formula for $\binom{n}{k}$ is $\binom{n}{k}=\frac{n!}{k!(n-k)!}$,
where $n!$ represents the factorial of $n$ (the product of all positive integers less than or equal to $n$).
For $\binom{11}{9}$, we have $\binom{11}{9}=\frac{11!}{9!(11-9)!}=\frac{11!}{9!2!}$.
Simplifying, we have $\frac{11!}{9!2!}=\frac{11\times10\times9!}{9!\times2\times1}=\frac{11\times10}{2\times1}=\boxed{55}$.
The answer is: 55
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What is the value of $\dbinom{11}{9}$?

### Answer:
