1. **Problem Statement:** We need to find the number of possible special plate numbers made up of 3 letters followed by 2 digits. 2. **Given:** - Plate format: 3 letters + 2 digits - Letters: English alphabet (26 letters) - Digits: 0 to 9 (10 digits) 3. **Part (a): Letters and digits can be repeated** - For each letter position, there are 26 choices. - For each digit position, there are 10 choices. - Since repetition is allowed, choices multiply directly. Number of plates = $26^3 \times 10^2$ Calculate: $$26^3 = 26 \times 26 \times 26 = 17576$$ $$10^2 = 10 \times 10 = 100$$ Total plates = $17576 \times 100 = 1,757,600$ 4. **Part (b): Letters and digits cannot be repeated** - For letters (3 positions): - First letter: 26 choices - Second letter: 25 choices (one letter used) - Third letter: 24 choices - For digits (2 positions): - First digit: 10 choices - Second digit: 9 choices (one digit used) Number of plates = $26 \times 25 \times 24 \times 10 \times 9$ Calculate: $$26 \times 25 = 650$$ $$650 \times 24 = 15600$$ $$15600 \times 10 = 156000$$ $$156000 \times 9 = 1,404,000$$ 5. **Final answers:** - (a) $1,757,600$ possible plates - (b) $1,404,000$ possible plates