AMC 12 2005b Problem 11

An envelope contains eight bills: $2$ ones, $2$ fives, $2$ tens, and $2$ twenties. Two bills are drawn at random without replacement. What is the probability that their sum is at least $\$20$?

\textbf{(A)}\ \frac{1}{4} \textbf{(B)}\ \frac{2}{7} \textbf{(C)}\ \frac{3}{7} \textbf{(D)}\ \frac{1}{2} \textbf{(E)}\ \frac{2}{3}