Mathematics
Grade 9
15 min
Combination and permutation notation
Combination and permutation notation
What you'll learn
- Multiply two fractions: Students will be able to accurately multiply two proper fractions and two improper fractions, expressing the product in simplest form, in at least 8 out of 10 problems.
- Simplify Fractions: Students will be able to identify the greatest common factor (GCF) of the numerator and denominator of a fraction and use it to simplify fractions before or after multiplying, correctly simplifying at least 7 out of 10 fractions.
- Apply fraction multiplication: Students will be able to solve word problems involving the multiplication of two fractions, demonstrating their understanding by correctly setting up the problem and finding the solution in at least 3 out of 4 problems.
- Model fraction multiplication: Students will be able to represent the multiplication of two fractions visually using area models or other diagrams, correctly illustrating the product in at least 2 out of 3 examples.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define factorial, permutation, and combination.
Differentiate between scenarios requiring permutations (order matters) and combinations (order does not matter).
Read, interpret, and write expressions using permutation notation, P(n, r).
Read, interpret, and write expressions using combination notation, C(n, r).
Evaluate numerical expressions involving factorial, permutation, and combination notation.
Apply the correct notation and formula to solve simple counting problems.
How many different ways can you and your two best friends stand in line for a photo? 📸 Does the order you stand in matter?
This lesson introduces you to powerful mathematical notations for counting arrangements and selections. You will learn about factorials, permutations (where order...
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Key Concepts & Vocabulary
TermDefinitionExample
FactorialThe product of an integer and all the positive integers below it. It is denoted by an exclamation mark (!). For example, n! means n × (n-1) × (n-2) × ... × 1. By definition, 0! = 1.5! = 5 × 4 × 3 × 2 × 1 = 120
PermutationAn arrangement of a set of objects in a specific order. In 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, Ann and Bob, is the same combination as choosing Bob and Ann. There is only one combination.
n (in notation)Represents the total number of distinct objects available to choose from in a set.In a group of 10 students, n = 10.
r (in...
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Core Formulas
Permutation Notation and Formula
P(n, r) = \frac{n!}{(n-r)!}
Use this formula to find the number of ways to arrange 'r' objects from a set of 'n' objects. This is used when the order of the arranged objects is important.
Combination Notation and Formula
C(n, r) = \frac{n!}{(r!(n-r)!)}
Use this formula to find the number of ways to choose 'r' objects from a set of 'n' objects. This is used when the order of the chosen objects does not matter.
4 more steps in this tutorial
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Challenging
The expression C(n, r) is always equal to which other combination expression?
A.C(n, n-r)
B.C(r, n)
C.C(n-r, r)
D.C(n, r-1)
Challenging
A student calculates C(12, 3) and gets an answer of 1320. The correct answer is 220. What part of the combination formula did they most likely forget?
A.The (n-r)! in the denominator
B.The r! in the denominator
C.The n! in the numerator
D.They used (n-r)! instead of r!
Challenging
If C(n, 2) = 45, what is the value of P(n, 2)?
A.45
B.22.5
C.47
D.90
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Frequently asked questions
What grade level is "Combination and permutation notation"?
Combination and permutation notation is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Combination and permutation notation?
You'll be able to: Multiply two fractions: Students will be able to accurately multiply two proper fractions and two improper fractions, expressing the product in simplest form, in at least 8 out of 10 problems; Simplify Fractions: Students will….
Is "Combination and permutation notation" 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 Combination and permutation notation?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.