1970 AHSME 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 is divisible by 11?

\textbf{(A) }2/5\qquad \textbf{(B) }1/5\qquad \textbf{(C) }1/6\qquad \textbf{(D) }1/11\qquad \textbf{(E) }1/15

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