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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.
Alfredo J. Romero C.
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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.
Solution: there are 5 printer: A-B-C-D-E Each printer can print any number of pages, there is no restriction, so there for every page, there are five printer options available.
. Page 1 = 5 options available. : Page 2 = 5 options available.
So total number of ways to assign 125 pages to five printer = 5*5*5 ... *5 (125 times!)
So 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?
Solution: Since the first and last pages need to be colored and there are only two colored printer.
So to print the rest of the pages (123 pages), since the two color printer can also print black and white, there are five printer available. there:
- total ways will be = 5123
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Now for the first and last page, there are only two printer available so the total way is: . = 22 = 4
: = So total ways = 5123 * 4
(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?
Solution: Now we have to rint consecutive 25 pages on the same printer. So out of the 125 pages first we have to divide them into group of 25 pages, and since the pages are consecutive the are five groups that will be formed. Similarly, each group can be printed in any of the 5 printer giving us the total of:
.5*5*5*5*5
= 55 = 3125 ways