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Ch. 8 - Sequences, Induction, and Probability
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 8 - Sequences, Induction, and ProbabilityProblem 84
Chapter 9, Problem 84

Use a calculator's factorial key to evaluate each expression. 20!/(20−3)!

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Identify the expression given: \(\frac{20!}{(20-3)!}\).
Simplify the denominator inside the factorial: calculate \(20 - 3\) to get \(17\), so the expression becomes \(\frac{20!}{17!}\).
Recall the definition of factorial: \(n! = n \times (n-1) \times (n-2) \times \cdots \times 1\).
Express \$20!\( in terms of \)17!$ to simplify the fraction: \(20! = 20 \times 19 \times 18 \times 17!\).
Cancel out \$17!$ in numerator and denominator, leaving \(20 \times 19 \times 18\), which you can then multiply using a calculator.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Factorials

A factorial, denoted 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 commonly used in permutations, combinations, and probability calculations.
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Permutation Formula

The expression 20! / (20−3)! represents the number of permutations of 20 items taken 3 at a time. It counts the ordered arrangements of 3 elements selected from 20, calculated by dividing the factorial of the total items by the factorial of the difference.
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Using a Calculator's Factorial Function

Many scientific calculators have a factorial key (!) to compute factorial values quickly. To evaluate expressions like 20!/(20−3)!, you calculate 20! and 17! separately or use the permutation function if available, simplifying the process and reducing manual errors.
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Related Practice
Textbook Question

In Exercises 81–85, use a calculator's factorial key to evaluate each expression.

54!(54−3)!3!\(\frac{54!}{(54-3)!3!}\)

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Textbook Question

Use a calculator's factorial key to evaluate each expression. (300/20)!

Textbook Question

Write an equation in point-slope form and slope-intercept form for the line passing through (-2, -6) and perpendicular to the line whose equation is x − 3y+ 9 = 0.

Textbook Question

Show that the sum of the first n positive odd integers,1 +3 +5 + ··· + (2n − 1), ... is n².

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Textbook Question

In Exercises 81–85, use a calculator's factorial key to evaluate each expression.

20!300\(\frac{20!}{300}\)

Textbook Question

In the sequence 21,700, 23,172, 24,644, 26,116,... which term is 314,628?