Domanda del libro di testo
Evaluate each expression.
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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 23
Evaluate each factorial expression. 17!/15!
Guida verificata passo dopo passo1
Recall the definition of factorial: for any positive integer \(n\), \(n! = n \times (n-1) \times (n-2) \times \cdots \times 1\).
Write out the factorial expressions explicitly: \(17! = 17 \times 16 \times 15!\).
Substitute this into the given expression: \(\frac{17!}{15!} = \frac{17 \times 16 \times 15!}{15!}\).
Notice that \$15!$ appears in both numerator and denominator, so they cancel out: \(\frac{17 \times 16 \times \cancel{15!}}{\cancel{15!}} = 17 \times 16\).
The expression simplifies to the product \(17 \times 16\), which you can multiply to find the final value.
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Factorial Notation
Factorial notation, denoted by n!, represents the product of all positive integers from n down to 1. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. It is commonly used in permutations, combinations, and other algebraic expressions.
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Factorials
Simplifying Factorial Expressions
When dividing factorials like 17!/15!, you can cancel common terms. Since 17! = 17 × 16 × 15!, the 15! terms cancel out, leaving 17 × 16. This simplification avoids calculating large factorials directly.
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5:22Factorials
Properties of Factorials in Division
Factorials have the property that n! = n × (n-1)!. This allows breaking down factorial expressions in division problems to simplify calculations by canceling out common factorial terms, making complex expressions manageable.
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5:22Factorials
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