Problem:
In the small country of Mathland, all automobile license plates have four symbols. The first must be a vowel , or , the second and third must be two different letters among the non-vowels, and the fourth must be a digit through . If the symbols are chosen at random subject to these conditions, what is the probability that the plate will read
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The first symbol can be any of the vowels, the second can be any of the consonants, the third can be any of the other consonants, and the fourth can be any of the digits. The total number of possible license plates is . Only one plate will read "", so the probability is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions