1. The problem is to evaluate the binomial coefficient $\binom{2}{2}$. 2. The binomial coefficient $\binom{n}{k}$ is defined as: $$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$ where $n!$ denotes the factorial of $n$. 3. Substitute $n=2$ and $k=2$ into the formula: $$\binom{2}{2} = \frac{2!}{2!(2-2)!} = \frac{2!}{2!\times 0!}$$ 4. Recall that $0! = 1$, so: $$\binom{2}{2} = \frac{2!}{2! \times 1}$$ 5. Calculate the factorials: $$2! = 2 \times 1 = 2$$ 6. Substitute the values: $$\binom{2}{2} = \frac{2}{2 \times 1} = \frac{2}{2}$$ 7. Simplify the fraction by canceling common factors: $$\binom{2}{2} = \frac{\cancel{2}}{\cancel{2}} = 1$$ 8. Therefore, the value of $\binom{2}{2}$ is 1.