Final answer:
To determine the number of possible Alaskan license plates with three letters and three single-digit numbers, multiply 26^3 (the possibilities for the letters) by 10^3 (the possibilities for the numbers). This results in 17,576,000 different possible license plates.
Step-by-step explanation:
The question involves calculating the number of different license plates possible for an Alaskan state license plate with a specific format. Here, the format is three letters followed by three single-digit numbers. Since letters and digits can be repeated, the calculation falls under the basic principle of counting in combinatorics, a branch of Mathematics.
For the three letters, each position can be any letter from A to Z, which gives us 26 possibilities for each of the three slots. Therefore, the number of possible combinations for the letters is 26 × 26 × 26. For the single-digit numbers, each one can be any digit from 0 to 9, which gives us 10 possibilities for each of the three positions. Therefore, the number of possible combinations for the numbers is 10 × 10 × 10.
To find the total number of different license plates possible, we multiply the possibilities for the letters by the possibilities for the numbers: (26 × 26 × 26) × (10 × 10 × 10), which equals 17,576,000 different license plates.