SOLUTION: 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 the third must be two different letters
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Question 1120140: 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 the 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 by greenestamps(13203) (Show Source):
There are 5 choices for the first symbol (it must be a vowel); there are (21*20) choices for the second and third symbols (two different non-vowel letters); and there are 10 choices for the fourth symbol (a digit 0-9).
The total number of license plates possible is (5)(21*20)(10) = 21000.
The license plate AMC8 is one of those possibilities; the probability is then 1/21000.
