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All license plates have a letter, two characters (which are either a number or a letter) Followed by two numbers. The letter choice for the first character can only be either an E,W,P,R,A,F OR U. How many license plates can be made? What is the probability of having one with a vowel?

so a possible valid choice could be R 2S 56

All cases = 7 x 36 x 36 x 10 x 10907200
Assuming 5 vowels
number of cases without a vowel
= 4 x 31 x 31 x 10 x 10 = 3844400

prob(of having a vowel) = 1 - 384400/1090700
= appr .576

check my arithmetic

Found a typo .... forgot the = sign

should be :

All cases = 7 x 36 x 36 x 10 x 10 = 907200

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