In Exercises 1–8, evaluate the given binomial coefficient.

Verified step by step guidance

1. Identify the binomial coefficient to be evaluated: $(\genfrac{}{}{0ex}{}{12}{1})$.
2. Recall the formula for a binomial coefficient: $(\genfrac{}{}{0ex}{}{n}{k})=\frac{n!}{k!(n-k)!}$.
3. Substitute the values of $n$ and $k$ into the formula: $(\genfrac{}{}{0ex}{}{12}{1})=\frac{12!}{1!(12-1)!}$.
4. Simplify the expression: $(\genfrac{}{}{0ex}{}{12}{1})=\frac{12!}{1!\cdot 11!}$.
5. Recognize that $12!=12\cdot 11!$, so the expression simplifies to $(\genfrac{}{}{0ex}{}{12}{1})=\frac{12\cdot 11!}{1!\cdot 11!}$.