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Chapter 10: Problem 73

Explain the Fundamental Counting Principle.

Short Answer

Expert verified
The Fundamental Counting Principle states that if event A can occur in 'm' ways and event B in 'n' ways, then 'A followed by B' can occur in m*n ways. For example, with a menu of 3 main dishes, 2 sides, and 4 desserts, there are 24 possible meals. Alternatively, a 4-digit pin with numbers from 0-9 has 10,000 possible combinations.

Step by step solution

01

Definition

The Fundamental Counting Principle (FCP) is a method to count the number of ways an event can happen. This principle states that if event A can occur in m ways, and event B can happen in n ways, then the event 'A followed by B' can occur in m*n ways.
02

Illustrate with an example

To illustrate this concept, let's consider an example. Let's say there are 3 different main dishes, 2 side dishes and 4 desserts to choose from a menu. According to FCP, the total number of ways to make a three-course meal (main dish, side dish, and dessert) would be 3 (for the main) * 2 (for the side) * 4 (for the dessert), which equals 24. So there are 24 different combinations for a three-course meal.
03

Another example

Let's consider another example. If you have a lock with a 4-digit pin and each digit can be from 0 to 9 (10 possibilities). The total number of possible pin combinations will be \(10 * 10 * 10 * 10 = 10,000\) possible combinations. This is because each digit of the pin can be selected in 10 ways, and according to FCP, we just multiply these together.

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