2025 AMC 10B Problem 22

A seven-digit positive integer is chosen at random. What is the probability that the number is divisible by 11, given that the sum of its digits is 61?

\textbf{(A)} \dfrac{3}{14} \qquad \textbf{(B)} \dfrac{3}{11} \qquad \textbf{(C)} \dfrac{2}{7} \qquad \textbf{(D)} \dfrac{4}{11} \qquad \textbf{(E)} \dfrac{3}{7}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.