Combinations and permutations

Learning Objectives Distinguish between situations requiring permutations (where order matters) and combinations (where order does not matter). Apply the Fundamental Counting Principle to determine the total number of outcomes in a sequence of events. Calculate the number of permutations of n objects taken r at a time using the formula P(n, r). Calculate the number of combinations of n objects taken r at a time using the formula C(n, r). Solve problems involving permutations with non-distinct items. Use combinations and permutations to calculate the probabilities of complex events. How many different 3-topping pizzas can you make from 8 available toppings? 🍕 Let's find out how to count the possibilities without listing them all! This tutorial explores the powerful mat...

TermDefinitionExample FactorialThe product of an integer and all the positive integers below it, denoted by an exclamation mark (!). For a non-negative integer n, n! = n * (n-1) * (n-2) * ... * 1. By definition, 0! = 1.5! = 5 × 4 × 3 × 2 × 1 = 120 Fundamental Counting PrincipleIf there are 'm' ways to perform one action and 'n' ways to perform a second action, then there are m × n ways to perform both actions in sequence.If you have 3 shirts and 4 pairs of pants, you have 3 × 4 = 12 possible outfits. PermutationAn arrangement of a set of objects in a specific order. In permutations, the order of the objects is critical.The arrangements 'ABC' and 'CBA' are two different permutations of the letters A, B, and C. CombinationA selection of items from a c...

Permutation Formula P(n, r) = n! / (n - r)! Use this formula to find the number of ways to arrange 'r' objects from a set of 'n' distinct objects, where the order of arrangement matters. Combination Formula C(n, r) = n! / (r! * (n - r)!) Use this formula to find the number of ways to choose 'r' objects from a set of 'n' distinct objects, where the order of selection does not matter. Permutations with Repetition n! / (n₁! * n₂! * ... * nₖ!) Use this to find the number of distinct permutations of 'n' objects where there are n₁, n₂, ..., nₖ identical objects of each type.