### Fundamental Counting Principle

Lesson by Mike McGarry
Magoosh Expert

Summary
The fundamental counting principle is a cornerstone concept in combinatorics, essential for solving various types of counting problems encountered in the GMAT exam.
• The principle posits that if a task can be divided into stages, with each stage having a distinct number of ways it can be completed, the total number of ways to complete the entire task is the product of the number of ways to complete each stage.
• Examples provided include calculating the number of possible meals from a set menu, the number of ways to arrange books on a shelf, and the number of possible steering committees from a group of employees.
• The principle is foundational for understanding more complex combinatorial concepts, such as permutations and factorials, which will be discussed in subsequent lessons.
• Real-world applications of the principle demonstrate its utility in solving practical problems, highlighting the vast numbers that can arise from combinatorial calculations.
• The importance of recognizing when order matters in counting problems is emphasized, as it significantly affects the calculation of possible outcomes.
Chapters
00:00
Introduction to the Fundamental Counting Principle
01:06
Applying the Principle to Real-World Problems
02:15
Expanding the Principle to Arrangement Problems
04:57
Understanding the Importance of Order in Counting

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