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

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