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counting and probability junior
Problem
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"?
(A)
(B)
(C)
(D)
Solution
There is one favorable case, which is the license plate says "AMC8." We must now find how many total cases there are. There are choices for the first letter (since it must be a vowel), choices for the second letter (since it must be of consonants), choices for the third letter (since it must differ from the second letter), and choices for the digit. This leads to total possible license plates. Therefore, the probability of a license plate saying "AMC8" is .
Final answer
B