A state license plate consists of 1 letter followed by 5 digits.

Question

1. How many different license plates can be made?
2. If no digit could be repeated, how many possible license plates would there be?
3. A witness to a crime saw the first letter and first three digits of a license plate correctly as
4. A463 but could not see the last two digits.
5. How many license plates could start with A463?

Answer 1

1. There are 26 letters and 10 digits. So 26 x 10 x 10 x 10 x 10 x 10
2. 26 numbers. 1st digit can choose from 10, 2nd from 9 (as we cant repeat 1st digit) etc, so 26 x 10 x 9 x 8 x 7 x 6
3. A463---. Last 3 digits can be chosen in 10 x 10 x 10 ways