Textbook Question
In Exercises 31–34, write the first five terms of each geometric sequence. a1 = 1/2, r = 1/2
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Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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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 31
Use the Fundamental Counting Principle to solve Exercises 29–40. 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?
Verified step by step guidance1
Identify the categories involved in the problem. Here, the categories are: type of drink, size of the drink, and flavor of the drink.
Determine the number of options in each category. There are 2 types of drinks (sodas or milk shakes), 4 sizes (small, medium, large, jumbo), and 5 flavors (vanilla, strawberry, chocolate, coffee, pistachio).
Apply the Fundamental Counting Principle, which states that if there are multiple categories of choices, the total number of combinations is the product of the number of options in each category.
Write the multiplication expression to find the total number of ways to order a drink: \(2 \times 4 \times 5\).
Multiply the numbers to find the total number of possible drink orders (do not calculate the final product here, just set up the expression).
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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 there are multiple independent choices to be made, the total number of outcomes is the product of the number of options for each choice. For example, if there are 2 drink types and 4 sizes, the total combinations for these two choices is 2 × 4.
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Fundamental Counting Principle
Independent Choices in Combinatorics
Independent choices mean that the selection of one option does not affect the selection of another. In this problem, choosing a drink type, size, and flavor are independent decisions, so their possibilities multiply to find the total number of unique orders.
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5:54Probability of Multiple Independent Events
Multiplication of Multiple Categories
When dealing with several categories (like drink type, size, and flavor), multiply the number of options in each category to find the total number of combinations. Here, multiply 2 (drinks) × 4 (sizes) × 5 (flavors) to get the total possible drink orders.
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03:42Finding Zeros & Their Multiplicity
Related Practice
Textbook Question
Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence. an = an-1 +3, a1 = 4
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Textbook Question
Find each indicated sum.
Textbook Question
Use mathematical induction to prove that each statement is true for every positive integer n. (ab)n = an bn
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Textbook Question
Write the first three terms in each binomial expansion, expressing the result in simplified form. (x+2)8
Textbook Question
Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
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