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License Plates in Mathland

Source: 2015 AMC 8 Problem 11

November 25, 2015
AMC 8

Problem Statement

In the small country of Mathland, all automobile license plates have four symbols. The first must be a vowel (A, E, I, O, or U), the second and third must be two different letters among the 21 non-vowels, and the fourth must be a digit (0 through 9). If the symbols are chosen at random subject to these conditions, what is the probability that the plate will read "AMC8"?
<spanclass=′latex−bold′>(A)</span>122,050<spanclass=′latex−bold′>(B)</span>121,000<spanclass=′latex−bold′>(C)</span>110,500<spanclass=′latex−bold′>(D)</span>12,100<spanclass=′latex−bold′>(E)</span>11,050 <span class='latex-bold'>(A) </span> \frac{1}{22,050} \qquad <span class='latex-bold'>(B) </span> \frac{1}{21,000}\qquad <span class='latex-bold'>(C) </span> \frac{1}{10,500}\qquad <span class='latex-bold'>(D) </span> \frac{1}{2,100} \qquad <span class='latex-bold'>(E) </span> \frac{1}{1,050}
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