1. **State the problem:** You have 20 possible questions, and the instructor will randomly pick 4 for the exam. You prepared exactly 4 questions. We want to find the probability that the 4 questions you prepared are exactly the ones chosen. 2. **Formula used:** The probability of selecting a specific set of 4 questions out of 20 is given by the ratio of favorable outcomes to total possible outcomes. Total ways to choose 4 questions from 20 is given by the combination formula: $$\binom{20}{4} = \frac{20!}{4!(20-4)!}$$ Since you prepared exactly 4 questions, there is only 1 favorable outcome (the exact set you prepared). 3. **Calculate total combinations:** $$\binom{20}{4} = \frac{20 \times 19 \times 18 \times 17}{4 \times 3 \times 2 \times 1} = \frac{116280}{24} = 4845$$ 4. **Calculate probability:** $$P = \frac{\text{favorable outcomes}}{\text{total outcomes}} = \frac{1}{4845}$$ 5. **Interpretation:** The probability that the 4 questions you prepared are exactly the ones chosen is very small, about 1 in 4845. **Final answer:** $$\boxed{\frac{1}{4845}}$$