/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 13 In Exercises 13-32, evaluate eac... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 13

In Exercises 13-32, evaluate each factorial expression. \(\frac{9 !}{6 !}\)

Short Answer

Expert verified
The evaluation of the expression \(\frac{9 !}{6 !}\) equals 504.

Step by step solution

01

Understanding the Factorial Function

Factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. Thus, \(9! = 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\) and \(6! = 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\). The given expression can then be written as \(\frac{9 \cdot 8 \cdot 7 \cdot 6!}{6!}\).
02

Cancelling Similar Terms

Notice we have \(6!\) in both the numerator and the denominator. Since any number divided by itself equals 1, \(6!\) in the numerator and the denominator will cancel out each other. Therefore, the expression simplifies to \(9 \cdot 8 \cdot 7\).
03

Calculating the Result

Now we just have to multiply the numbers together to get the final result. So, \(9 \cdot 8 \cdot 7 = 504\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The model of the car you are thinking of buying is available in nine different colors and three different styles (hatchback, sedan, or station wagon). In how many ways can you order the car?

An ice cream store sells two drinks (sodas or milk shakes), in four sizes (small, medium, large, or jumbo), and five flavors (vanilla, strawberry, chocolate, coffee, or pistachio). In how many ways can a customer order a drink?

If a single die is rolled twice, find the probability of rolling an odd number and a number greater than 4 in either order.

In how many different ways can a police department arrange eight suspects in a police lineup if each lineup contains all eight people?

A restaurant offers eight appetizers and ten main courses. In how many ways can a person order a two-course meal?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.