AMC 10B 2025 (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

\text{(A)}\;\frac{3}{14}

\text{(B)}\;\frac{3}{11}

\text{(C)}\;\frac{2}{7}

\text{(D)}\;\frac{4}{11}

\text{(E)}\;\frac{3}{7}