1. The problem asks for the value of the binomial coefficient $\binom{8}{9}$. 2. The binomial coefficient $\binom{n}{k}$ is defined as the number of ways to choose $k$ elements from a set of $n$ elements without regard to order. It is given by the formula: $$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$ 3. An important rule is that if $k > n$, then $\binom{n}{k} = 0$ because you cannot choose more elements than are available in the set. 4. Here, since $9 > 8$, we have $\binom{8}{9} = 0$. 5. Therefore, the value of $\binom{8}{9}$ is 0.