1. **State the problem:** We need to find the number of different voicemail passwords possible where each password consists of 1 letter followed by a 3-digit number less than 600. 2. **Understand the components:** - The first character is a letter. Assuming only uppercase English letters, there are 26 possibilities. - The next part is a 3-digit number less than 600. This means numbers from 000 to 599 inclusive. 3. **Calculate the number of 3-digit numbers less than 600:** - The smallest 3-digit number is 000 (considering leading zeros allowed). - The largest number less than 600 is 599. - Total numbers = 600 (from 0 to 599 inclusive). 4. **Calculate total passwords:** - For each letter (26 options), there are 600 possible numbers. - Total passwords = $26 \times 600 = 15600$. 5. **Final answer:** There are **15600** different voicemail passwords possible.