#### 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

Verified#### Step 1

1 of 5$a)$

Let consider $6$ blanks that need to be filled with the appropriate numbers and letters. In first place we can put one of $10$ digits, so the number of ways to choose one digit of $10$ digits is number of combinations, $C^{10}_1$. In the next three places we can put any letters of $26$ letters, because repetition is allowed. So, the number of ways we can fill any of the next three places is $C_1^{26}$. Finally, we fill the last two places with one of $10$ digits and we can do it in $C_1^{10}$ ways.