How many options are there for license plates with any three letters (A-Z) followed by any 3 numbers (0-9)?

• A. $260$
• B. $2340$
• C. $11,232,000$
• D. $17,576,000$

Answer: (D)

Verified step by step guidance

1. Identify the structure of the license plate: it consists of three letters followed by three numbers.
2. Calculate the number of possible combinations for the letters. Since there are 26 letters in the English alphabet, and each position can be any letter, the number of combinations for the letters is 26 * 26 * 26.
3. Calculate the number of possible combinations for the numbers. Since there are 10 digits (0-9), and each position can be any digit, the number of combinations for the numbers is 10 * 10 * 10.
4. Multiply the number of combinations for the letters by the number of combinations for the numbers to find the total number of possible license plates.
5. The formula for the total number of license plates is: $26\times 26\times 26\times 10\times 10\times 10$.