SOLUTION: 6. An Ontario license plate has 4 letters followed by 3 numbers. Assuming repetition is allowed, how many license plates a) contain only vowels and even numbers? [1] b) contain t

Algebra ->  Permutations -> SOLUTION: 6. An Ontario license plate has 4 letters followed by 3 numbers. Assuming repetition is allowed, how many license plates a) contain only vowels and even numbers? [1] b) contain t      Log On


   

Question 1191646: 6. An Ontario license plate has 4 letters followed by 3 numbers. Assuming repetition is allowed, how many license plates
a) contain only vowels and even numbers? [1]
b) contain the same 4 letters and the same 3 digits?
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.
6. An Ontario license plate has 4 letters followed by 3 numbers. Assuming repetition is allowed, how many license plates
a) contain only vowels and even numbers? [1]
b) contain the same 4 letters and the same 3 digits?
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To start, use this info 

    (1)  The English alphabet is made up of 26 letters, 5 of which are vowels (a, e, i, o, u) and the rest of which are consonants. 
    (2)  There are 5 even digits.


                        Therefore

Question (a) 

    how many license plates = 5%5E4.5%5E3 = 5%5E7 = 79125.     ANSWER


Question (b) 

        how many license plates of this special form = 26*10 = 260.     ANSWER

Solved.