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Chapter 11: Problem 75

What is a permutation?

Short Answer

Expert verified
A permutation refers to the arrangement or rearrangement of items in a specific order. It varies in types based on whether the arrangement allows repetition of elements or not. The term permutation also implies the action of changing the order of the elements in an ordered set.

Step by step solution

01

Definition

In mathematics, a permutation of a set is, loosely, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word 'permutation' also refers to the act or process of changing the linear order of an ordered set.
02

Distinguish from combinations

Permutations differ from combinations, which are selections of some members of a set with no regard to the order they are in when selected.
03

Permutations with repetition

When the members of a set can be repeated in a permutation, it is called a permutation with repetition. For example, in the set of numbers {1, 2}, the possible permutations with repetition for a sequence of two numbers are: {1, 1}, {1, 2}, {2, 1}, {2, 2}.
04

Permutations without repetition

When the members of a set cannot be repeated in a permutation, it is called a permutation without repetition. For example, in the set of numbers {1, 2}, the possible permutations without repetition for a sequence of two numbers are: {1, 2}, {2, 1}

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Most popular questions from this chapter

You select a family with three children. If \(M\) represents a male child and \(F\) a female child, the sample space of equally likely outcomes is \(\\{M M M, M M F, M F M, M F F, F M M FMF, FFM, FFF\)} - Find the probability of selecting a family with $$\text{at least two female children.}$$

Explaining the Concepts Explain how to find the probability of an event not occurring. Give an example.

You are dealt one card from a 52-card deck. Find the probability that you are dealt a 5 or a black card.

Exercises \(116-118\) will help you prepare for the material covered in the next section. In Exercises \(116-117\) show that $$1+2+3+\cdots+n=\frac{n(n+1)}{2}$$ is true for the given value of \(n\) $$ n=5: \text { Show that } 1+2+3+4+5=\frac{5(5+1)}{2} $$

In Exercises \(105-108\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If the \(n\) th term of a geometric sequence is \(a_{n}=3(0.5)^{n-1}\) the common ratio is \(\frac{1}{2}\)
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