4.2 Introducing Permutations and Factorial Notation

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F Math 12 4.2 Introducing Permutations and Factorial Notation p. 238 Name Date Goal: Use factorial notation to solve simple permutation problems. 1. permutation: An arrangement of distinguishable objects in a definite order. For example, the objects a and b have two permutations, and . 2. factorial notation: A concise representation ofthe product of consecutive natural numbers: 1! = 2! = 3! = 4! = ! = − 1 − 2 … 3 2 1 LEARN ABOUT the Math Naomi volunteers after school at a daycare centre in Whitehorse, Yukon. Each afternoon, around 4 p.m., she lines up her group of children at the fountain to get a drink of water. How many different arrangements of children can Naomi create for the lineup for the water fountain if there are six children in her group?

Transcript of 4.2 Introducing Permutations and Factorial Notation

Page 1: 4.2 Introducing Permutations and Factorial Notation

F Math 12 4.2 Introducing Permutations and

Factorial Notation p. 238 Name

Date

Goal: Use factorial notation to solve simple permutation problems. 1. permutation: An arrangement of distinguishable objects in a definite order. For example,

the objects a and b have two permutations, and .

2. factorial notation: A concise representation ofthe product of consecutive

natural numbers:

1! =

2! =

3! =

4! =

𝑛! = 𝑛 𝑛 − 1 𝑛 − 2 … 3 2 1

LEARN ABOUT the Math Naomi volunteers after school at a daycare centre in Whitehorse, Yukon. Each afternoon, around 4 p.m., she lines up her group of children at the fountain to get a drink of water.

How many different arrangements of children can Naomi create for the lineup for the water fountain if there are six children in her group?

Page 2: 4.2 Introducing Permutations and Factorial Notation

Example 1: Solving a counting problem where order matters (p. 238)

Determine the number of arrangements that six children can form while lining up to drink.

Example 2: Evaluating numerical expressions involving factorial notation (p. 240)

Evaluate the following:

a) 10! !"!!!!!

Page 3: 4.2 Introducing Permutations and Factorial Notation

• 0! is defined to be equal to

• Restrictions on 𝑛 if 𝑛! is defined:

For example: State the values of n for which each expression is defined, where 𝑛 ∈ 𝐼

a) (𝑛 − 3)! b) !!

(!!!)!

Example 3: Simplifying an algebraic expression involving factorial notation (p. 241)

Simplify where 𝑛 ∈ 𝑁.

a) 𝑛 + 3 𝑛 + 2 ! b) !!! !!!! !

Page 4: 4.2 Introducing Permutations and Factorial Notation

Example 4: Solving an equation involving factorial notation (p.242)

Solve !!

!!! != 90, where 𝑛 ∈ 𝐼

Page 5: 4.2 Introducing Permutations and Factorial Notation
Page 6: 4.2 Introducing Permutations and Factorial Notation

HW: 4.2 p. 243-243 #2, 3, 5, 6, 9, 12, 14 & 15


15.1 Permutations

15.1 Permutations

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11.2 Permutations

11.2 Permutations

Use factorial notation to solve simple permutation ...

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