Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
10. Combinatorics & Probability
Combinatorics
1:26 minutes
Problem 31b
Textbook Question
Textbook QuestionUse 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?
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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 'm' ways to do one thing and 'n' ways to do another, then there are m × n ways to perform both actions. This principle is essential for calculating the total number of combinations in scenarios where multiple choices are involved.
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Fundamental Counting Principle
Combinations of Choices
In this context, the customer has multiple independent choices: the type of drink (2 options), the size (4 options), and the flavor (5 options). The total number of combinations is found by multiplying the number of choices for each category, illustrating how different selections can be combined.
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Combinations
Multiplicative Counting
Multiplicative counting involves multiplying the number of choices available at each stage of decision-making. In this problem, the total number of drink orders is calculated by multiplying the number of drink types, sizes, and flavors, demonstrating how to systematically account for all possible outcomes.
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