Combinations and permutations are important concepts in probability and statistics. They arise in various contexts such as arranging objects, selecting items from a set, or assigning tasks to individuals. In this lesson, we will explore the basic principles of combinations and permutations, learn how to differentiate between them, and practice solving problems involving these concepts.

Key Concepts:

• Combinations: choosing items from a set without regard to order
• Permutations: choosing items from a set with regard to order
• Factorials: counting the number of ways to arrange objects in a particular order
• Multiplication principle: extending the concept of factorials to larger sets

Practice Problems:

1. A bag contains 5 red balls, 7 blue balls, and 3 green balls. If a ball is drawn at random from the bag, what is the probability that it is blue? That it is not green?
2. A group of 10 people wants to select 4 representatives for a committee. How many different committees can be formed if each person has an equal chance of being selected?
3. A restaurant offers 5 appetizers, 8 main courses, and 3 desserts. How many different meals can a customer choose from?

Tags: math-is-fun, sat-prep, probability, statistics