Fundamental Counting Principle

Definition

The Fundamental Counting Principle states that if there are $n$ ways to do one thing, and $m$ ways to do another, then there are $n \times m$ ways to do both. This principle is used to calculate the total number of outcomes in a sequence of events.

5 Must Know Facts For Your Next Test

1. The Fundamental Counting Principle can be extended to more than two events: if there are $a$, $b$, and $c$ ways to perform three actions respectively, then the total number of ways is $a \times b \times c$.
2. This principle is essential for solving problems involving permutations and combinations.
3. It simplifies the calculation of large sets by breaking them down into smaller, manageable parts.
4. When using this principle, it is important that each event's outcome does not affect the others (independence).
5. It can be applied to real-life scenarios such as determining possible passwords or seating arrangements.

Review Questions

• How would you use the Fundamental Counting Principle to determine the number of different outfits you can wear if you have 4 shirts and 3 pairs of pants?
• Explain how the Fundamental Counting Principle differs from permutations and combinations.
• If a restaurant offers 5 appetizers, 7 main courses, and 4 desserts, how many different three-course meals can you order?

Related terms

Permutation: An arrangement of objects in a specific order. The order matters in permutations.

Combination: A selection of items without considering the order. The order does not matter in combinations.

Probability: A measure of the likelihood that an event will occur. It ranges from 0 (impossible) to 1 (certain).