Question

NEW YORK

The standard configuration for a New York license
plate is 3 digits followed by 3 letters.
Source: New York State Department of Motor Vehicles
How many different license plates are possible
if digits and letters can be repeated?
234 ABC
O 1757600
1577600
12812904
11232000

Answer 1

Answer: 10^3 * 26^3 = 17576000

Explain:
We need to count the number of ways that we can make a license plate number that has 3 digits followed by 3 letters.

For a digit, there are 10 possible choices (0,1,2,3,...9).
For a letter there are 26 choices (a,b,c,...,z).

The license plate number has six slots.
The first three slots will have three digits. There are 10*10*10 = 1000 ways to make the first three digits.

The last three slots will have three letters. There are 26*26*26=17576 ways to make the last three letters.

Combine these by multiplying. So there are 17576000 license plates.