1. **State the problem:** Mrs. Coleman sampled a collection of books and found 819 with no damage, 66 with minor damage, and 37 with major damage. We want to estimate how many of the total 45,000 books have no damage or minor damage. 2. **Calculate the total number of books in the sample:** $$819 + 66 + 37 = 922$$ 3. **Calculate the number of books with no damage or minor damage in the sample:** $$819 + 66 = 885$$ 4. **Find the proportion of books with no or minor damage in the sample:** $$\frac{885}{922}$$ 5. **Use this proportion to estimate the number in the entire collection:** $$45,000 \times \frac{885}{922}$$ 6. **Calculate the estimate:** $$45,000 \times \frac{885}{922} = 45,000 \times 0.95987 = 43,194.15$$ 7. **Round to the nearest whole number:** $$43,194$$ **Final answer:** Mrs. Coleman should expect approximately **43,194** books to have no damage or minor damage in the collection.