Mathematics
Grade 9
15 min
Permutations
Permutations
What you'll learn
- Solve word problems involving finding a fraction of a whole number, demonstrating the ability to correctly calculate the answer in at least 4 out of 5 problems.
- Explain the relationship between multiplying a whole number by a fraction and finding a part of that whole number, using mathematical vocabulary like 'numerator,' 'denominator,' and 'product' in their explanation.
- Apply the concept of finding a fraction of a whole number to real-world scenarios, such as calculating discounts or dividing ingredients in a recipe, with at least 80% accuracy.
- Identify and correct errors in worked examples of finding a fraction of a whole number, providing a clear explanation of the mistake and the correct solution.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define a permutation as an arrangement where order matters.
Use the Fundamental Counting Principle to determine the total number of outcomes.
Calculate the value of expressions involving factorial notation.
Apply the permutation formula, P(n, r), to find the number of possible arrangements.
Distinguish between problems that require arranging all items (n!) and a subset of items (P(n, r)).
Solve word problems by modeling them as permutations.
How many different ways can you arrange the songs in your favorite 3-song playlist? 🎶 Let's find out without listing every single one!
This tutorial introduces permutations, a powerful mathematical tool for counting the number of ways to arrange items when the order is important. You will learn how to use facto...
2
Key Concepts & Vocabulary
TermDefinitionExample
PermutationAn arrangement of a set of distinct objects in a specific order. In a permutation, the order of the objects matters.The arrangements 'ABC' and 'CBA' are two different permutations of the letters A, B, and C.
FactorialThe product of a positive integer and all the positive integers less than it. It is denoted by an exclamation mark (!). By definition, 0! = 1.5! (read as '5 factorial') is 5 × 4 × 3 × 2 × 1 = 120.
Fundamental Counting PrincipleA rule used to count the total number of possible outcomes in a situation. If there are 'm' ways to do one thing and 'n' ways to do another, then there are m × n ways of doing both.If you have 3 shirts and 2 pairs of pants, you have 3 × 2 = 6 possible outfits.
Arrangement...
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Core Formulas
Factorial Notation
n! = n * (n-1) * (n-2) * ... * 2 * 1
Used to calculate the total number of ways to arrange 'n' distinct objects. For example, the number of ways to arrange 4 people in a line is 4!.
Permutation Formula
P(n, r) = n! / (n-r)!
Used to find the number of ways to choose and arrange 'r' objects from a set of 'n' distinct objects. 'n' is the total number of items, and 'r' is the number of items you are arranging.
4 more steps in this tutorial
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Challenging
In how many ways can 5 people (A, B, C, D, E) be seated in a row if persons A and B must sit next to each other?
A.24
B.48
C.120
D.72
Challenging
In how many ways can 4 boys and 3 girls be seated in a row if no two girls can sit together?
A.1440
B.5040
C.720
D.144
Challenging
How many ways can the letters of the word 'PROBLEM' be arranged if the first letter must be 'P' and the last letter must be 'M'?
A.5040
B.720
C.2
D.120
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Frequently asked questions
What grade level is "Permutations"?
Permutations is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Permutations?
You'll be able to: Solve word problems involving finding a fraction of a whole number, demonstrating the ability to correctly calculate the answer in at least 4 out of 5 problems; Explain the relationship between multiplying a whole number by a….
Is "Permutations" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Permutations?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.