Permutations

Learning Objectives Define a permutation as an arrangement where order matters. Use the Fundamental Counting Principle to determine the total number of outcomes. Calculate the value of expressions involving factorial notation. Apply the permutation formula, P(n, r), to find the number of possible arrangements. Distinguish between problems that require arranging all items (n!) and a subset of items (P(n, r)). Solve word problems by modeling them as permutations. How many different ways can you arrange the songs in your favorite 3-song playlist? 🎶 Let's find out without listing every single one! This tutorial introduces permutations, a powerful mathematical tool for counting the number of ways to arrange items when the order is important. You will learn how to use facto...

TermDefinitionExample PermutationAn arrangement of a set of distinct objects in a specific order. In a permutation, the order of the objects matters.The arrangements 'ABC' and 'CBA' are two different permutations of the letters A, B, and C. FactorialThe product of a positive integer and all the positive integers less than it. It is denoted by an exclamation mark (!). By definition, 0! = 1.5! (read as '5 factorial') is 5 × 4 × 3 × 2 × 1 = 120. Fundamental Counting PrincipleA rule used to count the total number of possible outcomes in a situation. If there are 'm' ways to do one thing and 'n' ways to do another, then there are m × n ways of doing both.If you have 3 shirts and 2 pairs of pants, you have 3 × 2 = 6 possible outfits. Arrangement...

Factorial Notation n! = n * (n-1) * (n-2) * ... * 2 * 1 Used to calculate the total number of ways to arrange 'n' distinct objects. For example, the number of ways to arrange 4 people in a line is 4!. Permutation Formula P(n, r) = n! / (n-r)! Used to find the number of ways to choose and arrange 'r' objects from a set of 'n' distinct objects. 'n' is the total number of items, and 'r' is the number of items you are arranging.