License plates in one state consist of a digit followed by 3 letters and then 2 digits. a. How many different plates are possible if repetition is allowed on a given license plate? b. How many different plates are possible if no repetition is allowed on a given license plate?
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Let consider blanks that need to be filled with the appropriate numbers and letters. In first place we can put one of digits, so the number of ways to choose one digit of digits is number of combinations, . In the next three places we can put any letters of letters, because repetition is allowed. So, the number of ways we can fill any of the next three places is . Finally, we fill the last two places with one of digits and we can do it in ways.