AHSME 1970 Problem 31

If a number is selected at random from the set of all five-digit numbers in which the sum of the digits is equal to 43, what is the probability that this number will be divisible by 11? $\text{(A) } \frac{2}{5} \text{(B) } \frac{1}{5} \text{(C) } \frac{1}{6} \text{(D) } \frac{1}{11} \text{(E) } \frac{1}{15}$