1. **Problem statement:** Calculate the binomial coefficient $\binom{8}{2}$. 2. **Formula:** The binomial coefficient $\binom{n}{k}$ is calculated by the formula: $$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$ where $n!$ denotes the factorial of $n$. 3. **Apply the formula:** For $n=8$ and $k=2$: $$\binom{8}{2} = \frac{8!}{2!(8-2)!} = \frac{8!}{2!6!}$$ 4. **Simplify factorials:** $$8! = 8 \times 7 \times 6!$$ So, $$\binom{8}{2} = \frac{8 \times 7 \times 6!}{2! \times 6!}$$ 5. **Cancel common factors:** $$\binom{8}{2} = \frac{8 \times 7 \times \cancel{6!}}{2! \times \cancel{6!}} = \frac{8 \times 7}{2!}$$ 6. **Calculate $2!$:** $$2! = 2 \times 1 = 2$$ 7. **Final calculation:** $$\binom{8}{2} = \frac{8 \times 7}{2} = \frac{56}{2} = 28$$ **Answer:** $\boxed{28}$