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Even integers from 200-700 made by the set {1,2,5,7,8,9}

Source: 2011 AMC A Problem 13

June 25, 2011
AMC

Problem Statement

How many even integers are there between 200 and 700 whose digits are all different and come from the set {1,2,5,7,8,9}?
<spanclass=latexbold>(A)</span>12<spanclass=latexbold>(B)</span>20<spanclass=latexbold>(C)</span>72<spanclass=latexbold>(D)</span>120<spanclass=latexbold>(E)</span>200<span class='latex-bold'>(A)</span>\,12 \qquad<span class='latex-bold'>(B)</span>\,20 \qquad<span class='latex-bold'>(C)</span>\,72 \qquad<span class='latex-bold'>(D)</span>\,120 \qquad<span class='latex-bold'>(E)</span>\,200