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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.
Noyal Reji Jacob
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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.
5 printers are listed A,B,C,D,E a) A printer can print any number of pagers and there's no restriction. So there are 5 printing options available Page 1 = 5 option Page 2 = 5 option, so the total number of ways to assign 125 pages to five printer = 5*5*5*...*5(125 times) so total ways = 5(125)
(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 printers can also print black and white. How many ways are there for the 125 pages to be assigned to the five printers?
First and last pages need to be colored and there's only 2 colored printers 123 pages needed to be print because the color printer can alse print the black and white there will be 5 more printers available Total ways to print will be 5(123) Thefirstandlastpagetherewillbe2printersavailablesothetotalways = 22 = 4 sototalways = (5123) * 4)
(c) Suppose that all the pages are black and white, but each group of 25 consecutive 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.
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How many ways are there for the 125 pages to be assigned to the five printers?
25 pages needed to printed on the same printer So out of 125 pages needs to be divided into 25pages since there are 5 groups 5 groups can be printed in any of 5 printer so total will be 5*5*5*5*5 = 55 = 3125ways