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Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 3 - ProbabilityProblema 3.RE.6
Capitolo 3, Problema 3.RE.6

In Exercises 5 and 6, use the Fundamental Counting Principle.
6. The state of Virginia's license plates have three letters and four digits. Assuming that any letter or digit can be used, how many different license plates are possible?

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Step 1: Understand the structure of the license plate. The license plate consists of three letters followed by four digits. Each letter can be any of the 26 letters in the English alphabet, and each digit can be any of the 10 digits (0 through 9).
Step 2: Use the Fundamental Counting Principle, which states that if one event can occur in 'm' ways and a second event can occur in 'n' ways, then the total number of ways both events can occur is m × n. Extend this principle to all positions on the license plate.
Step 3: Calculate the number of possibilities for the letters. Since there are three letters and each can be chosen independently, the total number of combinations for the letters is 26 × 26 × 26 (or 26^3).
Step 4: Calculate the number of possibilities for the digits. Since there are four digits and each can be chosen independently, the total number of combinations for the digits is 10 × 10 × 10 × 10 (or 10^4).
Step 5: Multiply the total number of combinations for the letters by the total number of combinations for the digits to find the total number of possible license plates. This is (26^3) × (10^4).

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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 total number of ways both events can occur is 'm × n'. This principle is essential for calculating the total combinations of outcomes in scenarios involving multiple independent choices.
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Fundamental Counting Principle

Permutations and Combinations

Permutations refer to the arrangement of items where the order matters, while combinations refer to the selection of items where the order does not matter. In the context of license plates, since the arrangement of letters and digits is significant, we focus on permutations to determine the total possible configurations.
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Permutations vs. Combinations

Counting Outcomes

Counting outcomes involves determining the total number of possible results in a given scenario. For the Virginia license plates, we calculate the number of choices for letters (26 options for each of the three letters) and digits (10 options for each of the four digits), and then multiply these choices to find the total number of unique license plates.
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Fundamental Counting Principle
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