교과서 질문
Write the first five terms of each geometric sequence. an = - 4a(n-1), a1 = 10
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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
9장, 문제 4
Use the formula for nPr to evaluate each expression. 10P4
검증된 단계별 안내1
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.
주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
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.
추천 영상:
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.
추천 영상:
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.
추천 영상:
7:11Introduction to Permutations
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