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.
jeffrey Scroggins
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.
(b) we have 5 printer that can print so if we divide up the work by 5 each we can see the each printer will print 25 pages each in total so with tat in mind if do 5 * 5 * 5 * 5 * 5 and repeat this combination 125 time or 5125 we can see that answer is has a po (c) 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?
(d) like the quest befoor except this time we add take two from the first 5 pages and 2 from the last 5 pages to get2 * 2 * 5125 or4 * 5125 as our answer
(e) 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?
is very simple since we already know from before we can split the printing between the 5 printer evenly by 5 so we do 5*5*5*5*5 or 55
PROBLEM 2
Ten kids line up for recess. The names of the kids are:
{Alex, Bobby, Cathy, Dave, Emy, Frank, George, Homa, Ian, Jim}
Let S be the set of all possible ways to line up the kids. For example, one order might be: (Frank, George,Homa,Jim, Alex,Dave, Cathy,Emy,Ian,Bobby) The names are listed in order from left to right, so Frank is at the front of the line and Bobby is at the end of the line.
Let T be the set of all possible ways to line up the kids in which George is ahead of Dave in the line. Note that George does not have to be immediately ahead of Dave. For example,