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Chapter 8: Problem 75

What is a permutation?

Short Answer

Expert verified
A permutation is the number of ways a set of objects, items, or numbers can be arranged in a specific order. It's used when arrangements are considered important.

Step by step solution

01

Understanding the Concept

Permutation is a mathematical term that represents the number of ways a set of objects, items, or numbers can be arranged in a specific order. In more concrete terms, if you're given a set of 'n' objects, a permutation of these objects is any possible arrangement of the objects in a line.
02

Examples to Illustrate the Concept

A good everyday example of permutation is the arrangement of books on a shelf. If you have 5 different books, and you want to know how many ways they can be arranged in a row on a shelf, this is precisely what a permutation tells you. Similarly, take the arrangement of letters in a word - for a 3-letter word like 'CAT', there are 6 possible permutations: CAT, CTA, ACT, ATC, TCA, and TAC.
03

Applying the concept

In math, the formula for permutation is usually applied when specific arrangements are important. This formula is given by the expression \(P(n, r) = n! / (n-r)!\), where \(n\) is the total number of items, \(r\) is the number of items to choose for each arrangement, and \(n!\) denotes the factorial of \(n\).

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Most popular questions from this chapter

Enough curiosities involving the Fibonacci sequence exist to warrant a flourishing Fibonacci Association, which publishes a quarterly journal. Do some research on the Fibonacci sequence by consulting the Internet or the research department of your library, and find one property that interests you. After doing this research, get together with your group to share these intriguing properties.

A mathematics exam consists of 10 multiple-choice questions and 5 open-ended problems in which all work must be shown. If an examinee must answer 8 of the multiple-choice questions and 3 of the open-ended problems, in how many ways can the questions and problems be chosen?

Determine whether each statement is true or false If the statement is false, make the necessary change(s) to produce a true statement. $$\sum_{-1}^{2}(-1) / 2-0$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I've noticed that the big difference between arithmetic and geometric sequences is that arithmetic sequences are based on addition and geometric sequences are based on multiplication.

The group should select real-world situations where the Fundamental Counting Principle can be applied. These could involve the number of possible student ID numbers on your campus, the number of possible phone numbers in your community, the number of meal options at a local restaurant, the number of ways a person in the group can select outfits for class, the number of ways a condominium can be purchased in a nearby community, and so on. Once situations have been selected, group members should determine in how many ways each part of the task can be done. Group members will need to obtain menus, find out about telephone-digit requirements in the community, count shirts, pants, shoes in closets, visit condominium sales offices, and so on. Once the group reassembles, apply the Fundamental Counting Principle to determine the number of available options in each situation. Because these numbers may be quite large, use a calculator.
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