Question

Evaluate each expression. $\frac{8 !}{5 !}$

   Evaluate each expression.
$\frac{8 !}{5 !}$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Elayn Martin-Gay 4th Edition

Chapter 14, Problem 12

Instant Answer

Solved by Expert Julie Silva

04/09/2020

Step 1

\[8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\] \[5! = 5 \times 4 \times 3 \times 2 \times 1\] Show more…

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Evaluate each expression. $\frac{8 !}{5 !}$

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Key Concepts

Factorials

A factorial is the product of all positive integers up to a given number n, denoted by n!. It is a fundamental concept in combinatorics and arithmetic, used to count arrangements and to simplify expressions involving products of consecutive integers.

Cancellation in Factorial Division

When dividing two factorials where the numerator is the factorial of a larger number than the denominator, many terms in the product cancel out. This property allows for significant simplification by expressing the larger factorial in terms of the smaller factorial.

Arithmetic Simplification

After canceling common terms in a factorial division, the resulting expression often reduces to a simple multiplication of a few consecutive integers. This step involves performing basic arithmetic operations to arrive at the final value.

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