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In how many ways can five airplanes line up for departure on a runway?
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Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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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
Use a calculator's factorial key to evaluate each expression. (300/20)!
Guida verificata passo dopo passo1
Identify the expression to evaluate: \(\left( \frac{300}{20} \right)!\).
Simplify the fraction inside the factorial: calculate \(\frac{300}{20}\).
Once simplified, rewrite the expression as \(n!\), where \(n\) is the result from the previous step.
Recall that the factorial function \(n!\) means the product of all positive integers from 1 up to \(n\), i.e., \(n! = n \times (n-1) \times (n-2) \times \cdots \times 1\).
Use a calculator's factorial key to compute the value of \(n!\) based on the simplified integer \(n\).
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Factorial Function
The factorial of a non-negative integer n, denoted n!, is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials grow very quickly and are commonly used in permutations, combinations, and probability.
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5:22
Factorials
Order of Operations
Order of operations dictates the sequence in which parts of a mathematical expression are evaluated. In the expression (300/20)!, you first perform the division inside the parentheses, then apply the factorial to the result. This ensures accurate calculation.
Video consigliato:
8:38Performing Row Operations on Matrices
Using a Calculator's Factorial Key
Many scientific calculators have a factorial function, often labeled as 'n!'. To evaluate expressions like (300/20)!, you first compute the division, then use the factorial key on the resulting integer. This simplifies calculations of large factorials.
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5:22Factorials
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