We appreciate your visit to Suppose that all the pages are black and white but each group of 25 consecutive pages 1 25 26 50 51 75 76 100 must. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
To determine the number of ways to assign 100 pages to four printers under the given constraints, we analyze the permutations of distributing these pages in multiples of 25 per printer, taking into account the indistinguishability of printers assigned the same number of pages.
Explanation:
The student is asking about the combinatorics of assigning 100 black-and-white pages to four printers with specific constraints. Each group of 25 consecutive pages must be assigned to the same printer, and each printer can be assigned in multiples of 25 pages, up to a maximum of 100 pages.
To solve this, we consider all possible distributions of 100 pages into 4 groups (for the printers) where each group is a multiple of 25. The main combinations would be (0,0,0,100), (0,0,25,75), (0,0,50,50), (0,25,25,50), and (25,25,25,25). But we have to account for the fact that printers are indistinguishable if they are assigned the same number of pages. Thus, some of these combinations will have multiple permutations.
For example, (0,0,25,75) can be arranged in 4 ways, as the printer with 75 pages is distinct, but the three with 0 pages are not. Similarly, (0,25,25,50) can have 6 permutations, as there are 3 different ways to arrange the two printers with 25 pages. The distribution (25,25,25,25) only has 1 possible permutation since all printers are assigned the same number of pages.
By calculating the permutations for each combination and then summing them, we can determine the total number of ways to assign the 100 pages to the four printers under the given constraints.
Thanks for taking the time to read Suppose that all the pages are black and white but each group of 25 consecutive pages 1 25 26 50 51 75 76 100 must. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
Using the fundamental counting theorem, it is found that there are 256 ways for the 100 pages to be assigned to the four printers.
Fundamental counting theorem:
States that if there are n things, each with [tex]n_1, n_2, …, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem, for each of the 4 groups of pages, there are 4 ways that they can be printed, and the groups are independent, hence [tex]n = 4, n_1 = n_2 = n_3 = n_4 = 4[/tex].
Thus:
[tex]N = 4 \times 4 \times 4 \times 4 = 4^4 = 256[/tex]
There are 256 ways for the 100 pages to be assigned to the four printers.
A similar problem is given at https://brainly.com/question/24067651
