Question

Define factorial notation and explain how to evaluate $10 !$

   Define factorial notation and explain how to evaluate $10 !$

College Algebra

College Algebra

R. David Gustafson,… 11th Edition

Chapter 8, Problem 67

Instant Answer

Solved by Expert Amy Jiang

07/06/2020

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In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. Show more…

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Define factorial notation and explain how to evaluate $10 !$

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Key Concepts

Factorial Notation

Factorial notation is a mathematical shorthand used to represent the product of all positive integers up to a given number. The notation n! (read as 'n factorial') defines the product n × (n-1) × (n-2) ... down to 1. It is commonly used in combinatorics, probability, and various other fields to simplify expressions involving products of consecutive integers.

Evaluating a Factorial Expression

Evaluating a factorial expression such as 10! involves multiplying the sequence of descending positive integers from 10 down to 1: 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1. This process iterates through the multiplication of each consecutive integer to obtain a final product, which is integral to computations in areas like permutations and combination formulas.

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