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Five Digit numbers that have a digital sum of 43

Source: 1970 AHSME Problem 31

April 16, 2014
probabilityAMC

Problem Statement

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 4343, what is the probability that this number is divisible by 1111?
<spanclass=latexbold>(A)</span>2/5<spanclass=latexbold>(B)</span>1/5<spanclass=latexbold>(C)</span>1/6<spanclass=latexbold>(D)</span>1/11<spanclass=latexbold>(E)</span>1/15<span class='latex-bold'>(A) </span>2/5\qquad<span class='latex-bold'>(B) </span>1/5\qquad<span class='latex-bold'>(C) </span>1/6\qquad<span class='latex-bold'>(D) </span>1/11\qquad <span class='latex-bold'>(E) </span>1/15