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

검증된 단계별 안내

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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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 are commonly used in permutations, combinations, and probability calculations.

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.

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.