Mathematics
Grade 9
15 min
Combination and permutation notation
Combination and permutation notation
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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.
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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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