1. **Problem Statement:** We want to find the probability of getting a specific license plate "ABC012" where the plate format is three letters (no duplicates) followed by three numbers (no duplicates). 2. **Understanding the problem:** - Letters are chosen from 26 letters without repetition. - Numbers are chosen from 10 digits (0-9) without repetition. - The plate "ABC012" is one specific arrangement. 3. **Total number of possible plates:** - Number of ways to choose 3 distinct letters from 26 and arrange them: $$26 \times 25 \times 24$$ - Number of ways to choose 3 distinct digits from 10 and arrange them: $$10 \times 9 \times 8$$ - Total plates: $$26 \times 25 \times 24 \times 10 \times 9 \times 8$$ 4. **Number of favorable outcomes:** - Only one plate matches exactly "ABC012". 5. **Probability formula:** $$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$ 6. **Calculate the probability:** $$\text{Probability} = \frac{1}{26 \times 25 \times 24 \times 10 \times 9 \times 8}$$ 7. **Simplify the denominator:** $$26 \times 25 = 650$$ $$650 \times 24 = 15600$$ $$15600 \times 10 = 156000$$ $$156000 \times 9 = 1,404,000$$ $$1,404,000 \times 8 = 11,232,000$$ 8. **Final answer:** $$\boxed{\frac{1}{11,232,000}}$$ This means the probability of getting the plate "ABC012" is one in 11,232,000.