Textbook Question
Find each indicated sum.
844
views
Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 9, Problem 29
Use the Fundamental Counting Principle to solve Exercises 29–40. The model of the car you are thinking of buying is available in nine different colors and three different styles (hatchback, sedan, or sport). In how many ways can you order the car?
Verified step by step guidance1
Identify the number of choices for each category. Here, there are 9 different colors and 3 different styles (hatchback, sedan, sport).
Recall the Fundamental Counting Principle, which states that if one event can occur in \( m \) ways and a second independent event can occur in \( n \) ways, then the total number of ways both events can occur is \( m \times n \).
Apply the principle by multiplying the number of color options by the number of style options: \( 9 \times 3 \).
Set up the expression for the total number of ways to order the car as \( \text{Total ways} = 9 \times 3 \).
Interpret the result as the total number of unique car orders possible, combining each color with each style.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Fundamental Counting Principle
The Fundamental Counting Principle states that if one event can occur in m ways and a second independent event can occur in n ways, then the two events together can occur in m × n ways. This principle helps calculate the total number of possible outcomes when multiple choices or events are combined.
Recommended video:
4:04
Fundamental Counting Principle
Independent Choices
Independent choices mean that the selection of one option does not affect the selection of another. In this problem, choosing a car color does not influence the choice of style, so the total number of combinations is the product of the number of color options and style options.
Recommended video:
5:54Probability of Multiple Independent Events
Multiplication of Options
When multiple categories of options are available, the total number of unique combinations is found by multiplying the number of choices in each category. Here, multiplying 9 colors by 3 styles gives the total ways to order the car.
Recommended video:
03:42Finding Zeros & Their Multiplicity
Related Practice
Textbook Question
In Exercises 23–28, evaluate each factorial expression. (2n+1)!/(2n)!
587
views
Textbook Question
Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises 25–30. Find the sum of the first 14 terms of the geometric sequence: - 3/2, 3, - 6, 12, ...
909
views
Textbook Question
Use mathematical induction to prove that each statement is true for every positive integer n. 6 is a factor of n(n + 1)(n + 2).
691
views
Textbook Question
Use mathematical induction to prove that each statement is true for every positive integer n.
736
views
Textbook Question
Use the Binomial Theorem to expand each binomial and express the result in simplified form. (2a + b)6
687
views