Combination and permutation notation

Learning Objectives Define permutation and combination in the context of counting problems. Differentiate between scenarios that require permutations (order matters) and combinations (order does not matter). Read, interpret, and write permutation notation (nPr) and combination notation (nCr). Define and calculate factorials as a fundamental component of counting principles. Apply the formulas for permutations and combinations to calculate the number of possible outcomes. Solve simple word problems by selecting the appropriate notation and formula. If you have 5 favorite songs, how many different ways can you order them on a playlist? 🎶 Let's find out! This tutorial introduces two powerful tools for counting: permutations and combinations. You will learn the special no...

TermDefinitionExample FactorialThe product of a whole number and all the whole numbers less than it, down to 1. It is denoted by an exclamation mark (!). By definition, 0! = 1.5! (read as '5 factorial') = 5 × 4 × 3 × 2 × 1 = 120. PermutationAn arrangement of a set of objects in a specific order. With permutations, the order of the objects matters.The permutations of the letters A and B are AB and BA. There are two distinct arrangements. CombinationA selection of items from a set where the order of selection does not matter.Choosing a team of two people from a group of Ann and Bob. There is only one combination: {Ann, Bob}. The team 'Bob, Ann' is the same as 'Ann, Bob'. n (in notation)Represents the total number of distinct items available in a set to choose f...

The Permutation Formula P(n, r) = nPr = \frac{n!}{(n-r)!} Use this formula when you need to find the number of ways to arrange 'r' items from a set of 'n' items, and the order of arrangement is important. The Combination Formula C(n, r) = nCr = \binom{n}{r} = \frac{n!}{r!(n-r)!} Use this formula when you need to find the number of ways to select 'r' items from a set of 'n' items, and the order of selection does not matter.