Question

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

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

College Algebra

College Algebra

R. David Gustafson,… 11th Edition

Chapter 8, Problem 16

Instant Answer

Solved by Expert Amy Jiang

07/06/2020

Step 1

Step 1: Rewrite the expression as: $$\frac{8 !}{5 !} = \frac{8 \times 7 \times 6 \times 5 !}{5 !}$$ Show more…

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

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Key Concepts

Simplification of Factorial Expressions

When dividing one factorial by another, many terms in the product cancel out. For example, in a quotient like n! divided by k! (with n > k), the k! in the denominator cancels out the corresponding product in n!, leaving only the product of integers from k+1 to n. This technique makes it easier to simplify and compute expressions involving factorials.

Factorial Notation

A factorial, denoted by an exclamation mark (n!), is the product of all positive integers up to and including a given number n. It is a fundamental concept in combinatorics, algebra, and mathematical analysis, and is used to calculate permutations, combinations, and various other products in mathematics.

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