snhu MODULE THREE PROBLEM SET This document is proprietary to Southern New Hampshire University. It and the problems within may not be posted on any non-SNHU website. Diego Alvarez 1
snhu Directions: Type your solutions into this document and be sure to show all steps for arriving at your solution. Just giving a final number may not receive full credit. PROBLEM 1 A 125-page document is being printed by five printers. Each page will be printed exactly once. (a) Suppose that there are no restrictions on how many pages a printer can print. How many ways are there for the 125 pages to be assigned to the five printers? One possible combination: printer A prints out pages 2-50, printer B prints out pages 1 and 51-60, printer C prints out 61-80 and 86-90, printer D prints out pages 81-85 and 91-100, and printer E prints out pages 101-125. - Page 1 = 5 available options. - Page 2 = 5 available options. - Page 3 = 5 available options ... It keeps going until page 125. So to assign 125 pages to five printers: Total ways = 5125 (b) Suppose the first and the last page of the document must be printed in color, and only two printers are able to print in color. The two color print- ers can also print black and white. How many ways are there for the 125 pages to be assigned to the five printers? We only need to color two pages and we only have two colored printers. There are five printers available since they can also print black and white, so the rest of the pages are 123: Total ways = 5123 We know there are only two printers available for the first and the last page: - 22 = 4 - Total ways will be: 5123 * 4
snhu (c) Suppose that all the pages are black and white, but each group of 25 con- secutive pages (1-25, 26-50, 51-75, 76-100, 101-125) must be assigned to the same printer. Each printer can be assigned 0, 25, 50, 75, 100, or 125 pages to print. How many ways are there for the 125 pages to be assigned to the five printers? We have 125 pages, it is necessary to group them in pages of 25, we know that they are consecutive so we have 5 groups of 25. So we have that: - 5 * 5 * 5 * 5 *5 = 55 = 3215