2004 Pascal Problem 23

A driver approaching a toll booth has exactly two quarters, two dimes and two nickels in his pocket. He reaches into his pocket and randomly selects two of these coins. What is the probability that the coins that he selects will be at least enough to pay the 30-cent toll?

\textbf{(A)}\ \frac{3}{5}\quad \textbf{(B)}\ \frac{2}{5}\quad \textbf{(C)}\ \frac{1}{3}\quad \textbf{(D)}\ \frac{3}{10}\quad \textbf{(E)}\ \frac{2}{3}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.