Permutations & Combinations
Grade None
Question:
<p>A book has 618 pages. To number the pages, how many times a typist has to press keys if every page is to be numbered manually?</p>
<p style="display:inline">1647</p>
<p style="display:inline">1746</p>
<p style="display:inline">1678</p>
<p style="display:inline">1867</p>
Step-by-Step Solution
Key Concept: The total number of keystrokes is calculated by partitioning page numbers into categories based on their digit counts and summing the products of the page counts in each category and their respective number of digits.
<p>Number of pages to be numbered with one digit numbers = 9<br />
Number of pages to be numbered with two-digit numbers = 90<br />
Number of pages to be numbered with three-digit numbers = 519<br />
Required number = 9 <span class="math-tex">\(\times\)</span> 1 + 90 <span class="math-tex">\(\times\)</span> 2 + 519 <span class="math-tex">\(\times\)</span> 3 = 1746</p>
Correct Answer: B