Question

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?

Solution

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a)a)

Let consider 66 blanks that need to be filled with the appropriate numbers and letters. In first place we can put one of 1010 digits, so the number of ways to choose one digit of 1010 digits is number of combinations, C110C^{10}_1. In the next three places we can put any letters of 2626 letters, because repetition is allowed. So, the number of ways we can fill any of the next three places is C126C_1^{26}. Finally, we fill the last two places with one of 1010 digits and we can do it in C110C_1^{10} ways.

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