The problem asks how many different license plates can be formed, given that each plate consists of three digits (from 0 to 9) followed by three letters. Numbers and letters are chosen at random, and replicates are allowed.

Steps to solve:

1. Digits: For the first three positions, each position can have any digit from 0 to 9. That's 10 possible choices per position.

   • Total for digits: $10 \times 10 \times 10 = 10^3 = 1000$.

2. Letters: For the next three positions, each position can have any letter from A to Z. Since there are 26 letters, each position has 26 choices.

   • Total for letters: $26 \times 26 \times 26 = 26^3 = 17,576$.

3. Total number of plates: Multiply the total possibilities for the digits and the letters. $1000 \times 17,576 = 17,576,000$

Thus, the number of different license plates that can be formed is 17,576,000.

Do you want further details or have any questions?

Related questions:

1. What if replicates weren't allowed—how would that change the number of plates?
2. How many plates could be made if there were only 24 letters available instead of 26?
3. How would the total change if plates had 4 digits followed by 2 letters?
4. What if the digits were limited to odd numbers only (1, 3, 5, 7, 9)?
5. How does the number of plates change if one digit and one letter are randomly chosen from a restricted pool?

Tip:

When dealing with combinations or permutations, always break the problem into manageable parts, like handling digits and letters separately, before combining results!