/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 8 Matthew works as a computer oper... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 8

Matthew works as a computer operator at a small university. One evening he finds that 12 computer programs have been submitted earlier that day for batch processing. In how many ways can Matthew order the processing of these programs if (a) there are no restrictions? (b) he considers four of the programs higher in priority than the other eight and wants to process those four first? (c) he first separates the programs into four of top priority, five of lesser priority, and three of least priority, and he wishes to process the 12 programs in such a way that the top-priority programs are processed first and the three programs of least priority are processed last?

Short Answer

Expert verified
The number of ways Matthew can order the processing of the programs is: part (a) has \(12!\) ways, part (b) has \(4! * 8!\) ways, and part (c) has \(4! * 5! * 3!\) ways.

Step by step solution

01

Solve part (a) - No Restrictions

Given 12 programs to process with no priority (no restrictions), these can be arranged in \(12!\) ways. Using the formula n!, where n is the number of elements to arrange, the solution becomes \(12!\) (From 12 to 1)
02

Solve part (b) - 4 Programs with Higher Priority

Given 4 higher priority programs, these should be processed first. There are \(4!\) ways to process these 4 programs and \(8!\) ways to process the remaining 8 programs. Therefore, there are \(4! * 8!\) total ways to process these programs in order.
03

Solve part (c) - Programs in three Different Priority Levels

Given the programs are separated into three groups of priorities (4 top, 5 lesser, 3 least), we arrange the top priority first, lower second and the least last. Hence, the arrangement becomes \(4! * 5! * 3!\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Mr. and Mrs. Richardson want to name their new daughter so that her initials (first, middle, and last) will be in alphabetical order with no repeated initial. How many such triples of initials can occur under these circumstances?

For every positive integer \(n\), show that $$ \left(\begin{array}{l} n \\ 0 \end{array}\right)+\left(\begin{array}{l} n \\ 2 \end{array}\right)+\left(\begin{array}{l} n \\ 4 \end{array}\right)+\cdots=\left(\begin{array}{l} n \\ 1 \end{array}\right)+\left(\begin{array}{l} n \\ 3 \end{array}\right)+\left(\begin{array}{l} n \\ 5 \end{array}\right)+\cdots $$

Due to their outstanding academic records, Donna and Katalin are the finalists for the outstanding physics student (in their college graduating class). A committee of 14 faculty members will each select one of the candidates to be the winner and place his or her choice (checked off on a ballot) into the ballot box. Suppose that Katalin receives nine votes and Donna receives five. In how many ways can the ballots be selected, one at a time, from the ballot box so that there are always more votes in favor of Katalin? [This is a special case of a general problem called, appropriately, the ballot problem. This problem was solved by Joseph Louis Fran莽ois Bertrand (1822-1900).]

In how many ways can Beth place 24 different books on four shelves so that there is at least one book on each shelf? (For any of these arrangements consider the books on each shelf to be placed one next to the other, with the first book at the left of the shelf.)

Find the value(s) of \(n\) in each of the following: (a) \(P(n, 2)=90\), (b) \(P(n, 3)=3 P(n, 2)\), and (c) \(2 P(n, 2)+50=P(2 n, 2)\).
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.