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”?
Answer Choices
A. \dfrac{1}{22,050}
B. \dfrac{1}{21,000}
C. \dfrac{1}{10,500}
D. \dfrac{1}{2,100}
E. \dfrac{1}{1,050}