1. The problem is to evaluate the expression $1 - \binom{6}{1} \times 2$. 2. Recall the binomial coefficient formula: $\binom{n}{k} = \frac{n!}{k!(n-k)!}$, which counts the number of ways to choose $k$ elements from $n$ elements. 3. Calculate $\binom{6}{1}$: $$\binom{6}{1} = \frac{6!}{1! \times 5!} = \frac{6 \times 5!}{1 \times 5!} = 6$$ 4. Substitute back into the expression: $$1 - 6 \times 2$$ 5. Multiply: $$6 \times 2 = 12$$ 6. Finally, subtract: $$1 - 12 = -11$$ 7. Therefore, the value of the expression is $-11$.