2005 AMC 10B Problem 15

There are $\binom82 = 28$ equally likely pairs. A sum of at least $\$20$ comes from both twenties ($1$ way), a twenty paired with any of the six smaller bills ($2 \cdot 6 = 12$ ways), or both tens ($1$ way). The probability is $$\dfrac{1 + 12 + 1}{28} = \dfrac{14}{28} = \dfrac12.$$ Thus, D is the correct answer.