Permutation and combination notation

Learning Objectives Define factorial, 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). Identify the values of 'n' (total items) and 'r' (items to choose) from a word problem. Use the formulas to calculate the values for given permutation and combination notations. Apply the correct notation to solve simple real-world counting problems. How many different ways can you choose 3 friends from a group of 10 to go to the movies? 🍿 Does the order you choose them in change the group that goes? This tutorial introduces you to a powerful mathematic...

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 arrangements (A, B, C) and (C, B, A) are two different permutations of the letters A, B, and C. CombinationA selection of a set of objects where the order of selection does not matter.Choosing the letters A, B, and C to form a group. The group {A, B, C} is the same as the group {C, B, A}, so it is only one combination. n (in notation)Represents the total number of distinct objects available in the set.In a problem about choosing 3 s...

Permutation Notation and Formula nPr = \frac{n!}{(n-r)!} Used to find the number of ways to choose and arrange 'r' objects from a set of 'n' objects. Use this when the order of the chosen objects is important. Combination Notation and Formula nCr = \frac{n!}{(r!)(n-r)!} Used to find the number of ways to choose 'r' objects from a set of 'n' objects. Use this when the order of the chosen objects does not matter.