Permutations

Learning Objectives Define a permutation as an arrangement of objects where order is important. Correctly use and calculate factorial notation (n!). Differentiate between problems where order matters (permutations) and where it does not. Calculate the number of permutations of 'n' distinct objects taken all at a time using the n! formula. Calculate the number of permutations of 'n' distinct objects taken 'r' at a time using the P(n, r) formula. Apply permutation formulas to solve real-world word problems. How many different ways can you and your two best friends finish a race in 1st, 2nd, and 3rd place? 🥇🥈🥉 The answer might surprise you! This lesson introduces permutations, which are all about counting the number of ways to arrange items in...

TermDefinitionExample PermutationAn arrangement of a set of objects in a specific, defined order. In a permutation, 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 represented by an exclamation mark (!).5! (read as '5 factorial') is 5 × 4 × 3 × 2 × 1 = 120. By definition, 0! = 1. OrderThe sequence or position of items relative to each other. For permutations, order is the most important characteristic.In an election for President and Vice President, electing 'Sarah as President and Mike as VP' is a different outcome (order) than 'Mike as President and Sarah as VP'. Arra...

Factorial Notation n! = n * (n-1) * (n-2) * ... * 2 * 1 Used to calculate the total number of ways to arrange 'n' distinct objects. It's the foundation for all permutation formulas. Permutations of n Objects (All at a time) P(n, n) = n! Use this formula when you are arranging ALL of the 'n' available objects. For example, finding how many ways 5 people can stand in a line of 5. Permutations of n Objects (Taken r at a time) P(n, r) = n! / (n-r)! Use this when you are selecting and arranging 'r' objects from a larger group of 'n' objects. For example, awarding 1st, 2nd, and 3rd place medals (r=3) to a group of 10 runners (n=10).