2021 Gauss 8 Problem 20

Ruby and Sam each roll a fair 6-sided die with the numbers 1, 2, 3, 4, 5, and 6 on its faces. Sam subtracts the number on his roll from the number on Ruby's roll. What is the probability that the result is a negative number?

\textbf{(A)}\ \frac{5}{18}\quad \textbf{(B)}\ \frac{5}{12}\quad \textbf{(C)}\ \frac{7}{12}\quad \textbf{(D)}\ \frac{1}{2}\quad \textbf{(E)}\ \frac{5}{6}

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 Gauss contests here.