Question

Eraluate each expression. $$\frac{9 !}{12 !}$$

   Eraluate each expression.
$$\frac{9 !}{12 !}$$

College Algebra

College Algebra

R. David Gustafson,… 11th Edition

Chapter 8, Problem 15

Instant Answer

Solved by Expert Amy Jiang

07/06/2020

Step 1

Step 1: Rewrite the expression by expanding the larger factorial in the denominator: $$\frac{9 !}{12 !} = \frac{9 !}{12 \times 11 \times 10 \times 9 !}$$ Show more…

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Eraluate each expression. $$\frac{9 !}{12 !}$$

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Key Concepts

Factorial Function

The factorial function, denoted by an exclamation mark (!), represents the product of all positive integers up to a given number. It is a fundamental concept in combinatorics and mathematical analysis, used to count the number of ways to arrange items or to define series and distributions.

Cancellation in Factorial Expressions

When dealing with ratios of factorials, common terms in the numerator and denominator can be cancelled to simplify the expression. This technique takes advantage of the fact that factorial expressions are products that build on each other, allowing for the removal of overlapping multiplication factors.

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