Final answer:
None of the provided answer options match the correct result of 195 pages containing the digit '1'. The question involves the inclusion-exclusion principle in mathematics to calculate the number of pages with a '1' in the page number, which requires breaking down the problem into hundreds, tens, and ones places.
Step-by-step explanation:
The subject of this question is about using the inclusion-exclusion principle in mathematics to determine the number of pages in a book that contain the digit 1 in the page number. Since the book has 500 pages, we need to count the number of pages that have at least one '1' in their page numbers.
To find this, we break down the problem:
- Pages with '1' at the hundreds place: 100 to 199 (100 pages).
- Pages with '1' at the tens place: 10, 11, ..., 19, 110, 111, ..., 119, ..., 410, 411, ..., 419. (10 pages x 5 = 50 pages)
- Pages with '1' at the ones place: 1, 11, 21, ..., 91, 101, 111, ..., 491 (Same 10 occurrences per 100 pages x 5 = 50 pages).
However, pages with '11' at the tens and ones place are counted twice, so subtract 5 pages (11, 111, 211, 311, 411).
Adding these together:
- 100 + 50 + 50 - 5 = 195 pages contain the digit '1'.
None of the answer options A, B, C, D match this result, indicating that there may be an error in the provided options or the question itself.