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License plates in the newly established state of Atlantis consist of three letters followed by three digits. The first letter must be a vowel (y is not considered a vowel), and no letter can be repeated. The first digit must be one of {1,2,4,6}, which corresponds to the location the license was issued. No digit may be repeated. How many possible license plates exist?

 Jun 1, 2021
 #1
avatar+121056 
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We  have two jobs.....find all the possible combos of  vowels.....find all the possible digir combos

 

We   have   5 * 4 * 3   =  60  possible  combos of  vowels

 

And  we  have   4 * 3 * 2    =  24  possible combos of digits

 

So

 

Number of ways to  do  both jobs  = 

 

60  *  24    =   1440  possible plates

 

cool cool cool

 Jun 1, 2021

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