Factorial Notation:
In the application of the fundamental counting principle we spend a lot of time finding the product
of sequences of decreasing consecutive natural numbers.
i.e 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
For larger numbers this process gets tiresome, so a shorthand known as factorial notation is used to
condense 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 to 13! which reads as “13
factorial”
Similarly:
5! = 5 × 4 × 3 × 2 × 1
And 𝑛! = 𝑛 × (𝑛 − 1) × (𝑛 − 2) × (𝑛 − 3) × (𝑛 − 4) × … × 1
There is a factorial button on your calculator: Casio FX 82ZA
Above the button 𝑥−1 , in yellow is the text “𝑥! ", to access this function press SHIFT followed
𝑥−1
by
Example:
Evaluate 5! on your calculator.
𝑥−1 =
Press 5 + SHIFT + followed by
The display on your calculator will read 120
∴ 5! = 120
NOTE:
0! = 1
Your calculators only have enough memory to calculate up to 69! Anything higher will return
the message of “Math ERROR”. When asked to work with larger values than 69! The
expression must be simplified first before a calculator can be used.
EXERCISES:
Classroom Mathematics Exercise 13.5 pg 365
In the application of the fundamental counting principle we spend a lot of time finding the product
of sequences of decreasing consecutive natural numbers.
i.e 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
For larger numbers this process gets tiresome, so a shorthand known as factorial notation is used to
condense 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 to 13! which reads as “13
factorial”
Similarly:
5! = 5 × 4 × 3 × 2 × 1
And 𝑛! = 𝑛 × (𝑛 − 1) × (𝑛 − 2) × (𝑛 − 3) × (𝑛 − 4) × … × 1
There is a factorial button on your calculator: Casio FX 82ZA
Above the button 𝑥−1 , in yellow is the text “𝑥! ", to access this function press SHIFT followed
𝑥−1
by
Example:
Evaluate 5! on your calculator.
𝑥−1 =
Press 5 + SHIFT + followed by
The display on your calculator will read 120
∴ 5! = 120
NOTE:
0! = 1
Your calculators only have enough memory to calculate up to 69! Anything higher will return
the message of “Math ERROR”. When asked to work with larger values than 69! The
expression must be simplified first before a calculator can be used.
EXERCISES:
Classroom Mathematics Exercise 13.5 pg 365
