Domanda del libro di testo
Use a calculator's factorial key to evaluate each expression. (300/20)!
927
views
Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- 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
Capitolo 9, Problema 82
In how many ways can five airplanes line up for departure on a runway?
Guida verificata passo dopo passo1
Recognize that this is a permutation problem because the order in which the airplanes line up matters.
Recall the formula for permutations of n distinct objects: P(n) = n! (n factorial).
Identify the number of airplanes, which is 5. This means we need to calculate 5! (5 factorial).
Expand the factorial expression: 5! = 5 × 4 × 3 × 2 × 1.
Multiply the numbers in the factorial expression to determine the total number of ways the airplanes can line up.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
2mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Permutations
Permutations refer to the different arrangements of a set of items where the order matters. In this context, the five airplanes can be arranged in various sequences for departure, and each unique sequence is considered a different permutation. The formula for calculating permutations of 'n' items is n!, which represents the product of all positive integers up to 'n'.
Video consigliato:
7:11
Introduction to Permutations
Factorial
The factorial of a non-negative integer 'n', denoted as n!, is the product of all positive integers from 1 to n. Factorials are essential in combinatorial problems, such as determining the number of ways to arrange items. For example, 5! equals 5 × 4 × 3 × 2 × 1, which equals 120, representing the total arrangements of five airplanes.
Video consigliato:
5:22Factorials
Combinatorial Counting
Combinatorial counting involves techniques used to count the number of ways to arrange or select items from a set. In this scenario, we are interested in counting the arrangements of airplanes, which falls under permutations. Understanding combinatorial principles helps in solving problems related to arrangements, selections, and distributions in various mathematical contexts.
Video consigliato:
4:04Fundamental Counting Principle
Pratica correlata
Domanda del libro di testo
Use the Binomial Theorem to expand and then simplify the result: (x2 +x+ 1)3.
720
views
Domanda del libro di testo
In Exercises 81–85, use a calculator's factorial key to evaluate each expression.
918
views
Domanda del libro di testo
In Exercises 81–85, use a calculator's factorial key to evaluate each expression.
919
views
Domanda del libro di testo
In the sequence 21,700, 23,172, 24,644, 26,116,... which term is 314,628?
852
views
Domanda del libro di testo
Find the term in the expansion of (x2 + y2)5 containing x4 as a factor.
572
views