Permutations

Learning Objectives Define a permutation and explain why order is a critical component. Understand and correctly use factorial notation (n!) in calculations. Calculate the number of permutations of 'n' distinct objects taken all at a time. Calculate the number of permutations of 'n' distinct objects taken 'r' at a time using the permutation formula. Differentiate between problems that require permutations and those that do not. Solve real-world word problems involving permutations. How many different ways can you arrange the top 3 songs on your favorite playlist? 🎶 The answer might surprise you! This tutorial introduces permutations, a fundamental concept in probability for counting arrangements where order matters. You will learn how to use f...

TermDefinitionExample PermutationAn arrangement of a set of objects in a specific, definite order. In permutations, changing the order creates a new arrangement.The arrangements (A, B, C) and (C, B, A) are two different permutations of the letters A, B, and C. FactorialThe product of a whole number and all the whole numbers less than it, down to 1. It is denoted by an exclamation mark (!).5! (read as '5 factorial') is 5 × 4 × 3 × 2 × 1 = 120. By definition, 0! = 1. Distinct ObjectsItems or elements that are all unique and different from one another.The letters in the word 'MATH' (M, A, T, H) are distinct. The letters in 'BOOK' (B, O, O, K) are not all distinct because 'O' is repeated. ArrangementThe specific sequence or order in which a group of ite...

Factorial Notation n! = n * (n-1) * (n-2) * ... * 2 * 1 Used to find the total number of ways to arrange 'n' distinct objects. It is the foundation for all permutation calculations. Permutations of n Objects (all at a time) P(n, n) = n! This formula calculates the number of ways to arrange ALL 'n' objects from a set of 'n' distinct objects. For example, arranging 5 people in 5 chairs. Permutations of n Objects taken r at a time P(n, r) = n! / (n-r)! This is the general permutation formula. It calculates the number of ways to choose AND arrange 'r' objects from a larger set of 'n' distinct objects. For example, choosing and ranking the top 3 winners from 10 contestants.