4.1.2
Factorials
Factorial Notation
Factorial Notation
Factorial notation is used as shorthand for certain products of numbers.
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Factorials
Factorials
- The factorial of a number is equal to the number multiplied by all of the natural numbers smaller than it:
- For example, 4 factorial is equal to 4 × 3 × 2 × 1 = 24.
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Factorial notation
Factorial notation
- Factorial notation makes writing factorials easier.
- The factorial of a whole number is written as .
- 6 factorial =
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Factorials
Factorials
- The factorial of 0 is defined to be equal to 1.
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Applications
Applications
- Factorials are used in many areas of maths. One common use of factorials is counting the number of ways to pick or arrange objects.
- For example, if you have 3 unique items, the number of ways to arrange these items is equal to .
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Applications
Applications
- We can use factorials to work out the number of ways to pick distinct objects from a collection of objects.
- This number is called " choose
" and is
written as or
:
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Example
Example
- A restaurant offers five side dish options. Your meal comes with two side dishes.
- How many ways can you select your side dishes?
- The total number of options , and
, so we work out
:
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Connection to Pascal's triangle
Connection to Pascal's triangle
- We can work out each number in each row of Pascal's triangle using .
- The th number in the
th row of Pascal's triangle is equal to:
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Example
Example
- The 3rd number of the 4th row in Pascal's triangle is equal to:
1Proof
1.1Types of Numbers
1.2Notation
2Algebra & Functions
2.1Powers & Roots
2.2Quadratic Equations
2.3Inequalities
2.4Polynomials
2.5Graphs
2.7Transformation of Graphs
3Coordinate Geometry
3.1Straight Lines
3.2Circles
3.2.1Equations of Circles centred at Origin
3.2.2Finding the Centre & Radius
3.2.3Equation of a Tangent
3.2.4Circle Theorems - Perpendicular Bisector
3.2.5Circle Theorems - Angle at the Centre
3.2.6Circle Theorems - Angle at a Semi-Circle
3.2.7Equation of a Perpendicular Bisector
3.2.8Equation of a Circumcircle
3.2.9Circumcircle of a Right-angled Triangle
3.3Parametric Equations (A2 only)
4Sequences & Series
4.1Binomial Expansion
5Trigonometry
5.2Trigonometric Functions
5.3Triangle Rules
6Exponentials & Logarithms
6.1Exponentials & Logarithms
7Differentiation
7.1Derivatives
7.2Graphs & Differentiation
7.3Differentiation With Trigonometry and Exponentials
7.4Rules of Differetiation (A2 only)
7.5Parametric & Implicit Differentiation
8Integration
8.1Integration
9Numerical Methods
9.1Finding Solutions
9.2Finding the Area
10Vectors
10.12D Vectors
10.23D Vectors
10.3Vector Proofs
Jump to other topics
1Proof
1.1Types of Numbers
1.2Notation
2Algebra & Functions
2.1Powers & Roots
2.2Quadratic Equations
2.3Inequalities
2.4Polynomials
2.5Graphs
2.7Transformation of Graphs
3Coordinate Geometry
3.1Straight Lines
3.2Circles
3.2.1Equations of Circles centred at Origin
3.2.2Finding the Centre & Radius
3.2.3Equation of a Tangent
3.2.4Circle Theorems - Perpendicular Bisector
3.2.5Circle Theorems - Angle at the Centre
3.2.6Circle Theorems - Angle at a Semi-Circle
3.2.7Equation of a Perpendicular Bisector
3.2.8Equation of a Circumcircle
3.2.9Circumcircle of a Right-angled Triangle
3.3Parametric Equations (A2 only)
4Sequences & Series
4.1Binomial Expansion
5Trigonometry
5.2Trigonometric Functions
5.3Triangle Rules
6Exponentials & Logarithms
6.1Exponentials & Logarithms
7Differentiation
7.1Derivatives
7.2Graphs & Differentiation
7.3Differentiation With Trigonometry and Exponentials
7.4Rules of Differetiation (A2 only)
7.5Parametric & Implicit Differentiation
8Integration
8.1Integration
9Numerical Methods
9.1Finding Solutions
9.2Finding the Area
10Vectors
10.12D Vectors
10.23D Vectors
10.3Vector Proofs
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