Textbook Question
Write the first four terms of each sequence whose general term is given.
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Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 9, Problem 4
Use the formula for nPr to evaluate each expression. 10P4
Verified step by step guidance1
Recall the formula for permutations: \(\displaystyle {}_nP_r = \frac{n!}{(n-r)!}\), where \(n\) is the total number of items and \(r\) is the number of items to arrange.
Identify the values of \(n\) and \(r\) from the problem: here, \(n = 10\) and \(r = 4\).
Substitute these values into the permutation formula: \(\displaystyle {}_{10}P_4 = \frac{10!}{(10-4)!} = \frac{10!}{6!}\).
Simplify the factorial expression by expanding \$10!\( only as far as needed to cancel with \)6!$: \(\displaystyle \frac{10 \times 9 \times 8 \times 7 \times 6!}{6!}\).
Cancel the \$6!$ terms and multiply the remaining numbers: \(10 \times 9 \times 8 \times 7\) to find the number of permutations.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Permutation Formula
The permutation formula, denoted as nPr, calculates the number of ways to arrange r objects from a set of n distinct objects where order matters. It is given by nPr = n! / (n - r)!, where '!' denotes factorial.
Recommended video:
7:11
Introduction to Permutations
Factorial Function
A factorial, represented by n!, is the product of all positive integers from 1 up to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials are essential in permutations and combinations to count arrangements.
Recommended video:
5:22Factorials
Evaluating Permutations
To evaluate a permutation like 10P4, substitute into the formula: 10P4 = 10! / (10 - 4)! = 10! / 6!. Simplify by canceling common factorial terms and compute the product of the remaining factors.
Recommended video:
7:11Introduction to Permutations
Related Practice
Textbook Question
Use the formula for nPr to evaluate each expression. 8P5
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Textbook Question
Write the first six terms of each arithmetic sequence.
Textbook Question
A statement Sn about the positive integers is given. Write statements S1, S2 and S3 and show that each of these statements is true. Sn: 3 is a factor of n3 - n.
Textbook Question
Evaluate the given binomial coefficient.
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Textbook Question
Write the first four terms of each sequence whose general term is given. an=(−3)n
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