In Exercises 81–85, use a calculator's factorial key to evaluate each expression.
$the fraction with numerator 20 factorial and denominator 300$

검증된 단계별 안내

Recognize that the expression involves the factorial of 20, written as

20!

, which means the product of all positive integers from 1 to 20.

Understand that the expression to evaluate is

\frac{20!}{300}

, which means you need to divide the factorial of 20 by 300.

Use a calculator with a factorial function to compute

20!

. This will give you a very large number since factorials grow rapidly.

After finding the value of

20!

, perform the division by 300 to simplify the expression.

Write the final answer as the quotient of

20!

divided by 300, which completes the evaluation.

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주요 개념

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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 grow very quickly and are commonly used in permutations, combinations, and probability.

Using a Calculator's Factorial Function

Many scientific calculators have a factorial key (!) that allows quick computation of factorial values without manual multiplication. To evaluate expressions like 20!, you input 20 and then press the factorial key, which returns the exact or approximate value.

Simplifying Factorial Expressions

When dividing factorials or factorials by numbers, it’s important to understand how to simplify the expression. For example, 20!/300 means calculating 20! first, then dividing by 300. Recognizing when to simplify before calculating can save time and reduce errors.

In Exercises 81–85, use a calculator's factorial key to evaluate each expression.20!300\(\frac{20!}{300}\)