For the digits, you have 26 choices for the first and 26 choices for the second, giving you

26 * 26 = 676 possible combinations of letters.

Put them together and you have

1000 * 676 = 676,000 possible license plates.

Edit: sdatary (or whatever) is right. My bad.

There are 1000 three-digit combinations (000-999).

There are 650 two-letter combinations. To get this number, you need the formula for permutations which is nPr = (n!)/(n-r)!

n is the number of possible values for each element (in our case, 26, since there’s 26 letters in the alphabet).

r is the number of elements for each permutation (in our case, 2, since each license plate plate has two letters on it).

! is the factorial sign. For example 5! = 5 * 4 * 3 * 2 * 1… it’s easier if you have a calculator to do this calulation for.

Anyhow, you end up with 26 P 2 = (26!) / (26-2)! = 650

The reason that Diana got 676 is that her calculation double-counts the combinations AA, BB, CC, DD, EE… etc. There are 26 of these.

To get the total number of license plate combinations, multiply the number of “number” combinations by the number of “letter” combinations to get 650,000.