Basic Binomial Expansions

Binomial Expansion: Simple Examples

Prologue to Binomial Theorem (Arrangements)

Binomial Theorem & Pascal's Triangle

Binomial Theorem: Introductory Exercises

Proving Binomial Identities

Binomial Identities: Pascal Example

Greatest Coefficient in Binomial Expansion

Evaluating Coefficients From Two Expansions

Evaluating Specific Binomial Coefficients

Proving Binomial Identities: Comparing Coefficients

Pascal's Identity (1 of 2)

Pascal's Identity (2 of 2)

Arrangements of PERMUTATION with vowels in order

Another reason why 0! = 1 (thinking about arrangements)

Why is 0! = 1?

10 Socks Probability Problem (1 of 3: An Explanation I Dislike)

10 Socks Probability Problem (2 of 3: Explaining w/ Probability Trees)

10 Socks Probability Problem (3 of 3: Considering Permutations)

Introduction to Permutations (Ordered Selections)

Permutations: how do we account for repetitions?

Permutations: The Special Case of nPn

Introduction to Combinations (Unordered Selections)

Combinations Example 1: 4 Digits

Combinations Example 2: Two Teams + Umpire (1 of 2: No Restrictions)

Combinations Example 2: Two Teams + Umpire (2 of 2: Separate Players)

10 Boys & Girls Round a Table (1 of 2: Simple Conditions)

10 Boys & Girls Round a Table (2 of 2: Trickier Conditions)

Introduction to Circular Arrangements

Binomial Probability (1 of 2: Preliminary Example w/ Probability Tree)

Binomial Probability (2 of 2: Further Example & General Case)

Chance of a Pair in a Poker Hand

Binomial Probability: Defective shirts in a box

Interesting Permutations Question: Summing 3-Digit Numbers

Binomial / Permutations & Combinations Proof (1 of 2)

Binomial / Permutations & Combinations Proof (2 of 2)

Binomial Coefficients & Pascal's Triangle

Binomial Expansions - Simple Example

Why Notation & Terminology Are Awesome, Not Boring

nCr Notation

Sigma Notation & Properties of Pascal's Triangle

Approximating a Decimal Expansion with Binomial Theorem

Why do all rows of Pascal's triangle add to powers of 2?

Introduction to Factorial Notation (1 of 2: Why use "!"?)

Introduction to Factorial Notation (2 of 2: How to simplify factorial terms)

Shorthand Notation for nCr

Developing the Binomial Theorem w/ Pascal's Triangle

Stating the Binomial Theorem w/ Factorial Notation

Separating Rational & Irrational Components in Binomial Expansion

Expanding Binomials Involving Substitution

Identifying the Constant Term in a Binomial Expansion

Recognising & Substituting Part of a Binomial Expansion

Simplifying Products w/ Factorial Notation

What power of 2 is a factor of "100!"?

Summing Binomial Coefficients (Exam Question)

Evaluating Specific Binomial Coefficients (Exam Questions)

Binomial Coefficients Proof Question

Binomial Theorem (Finding a specified term using Commutations and a general Index Notation )

Binomial Theorem (1 of 2: Applications of Binomial Theorem and Binomial Identities)

Binomial Theorem (2 of 2: Finding the constant term in a binomial expansion)

Greatest Coefficient (1 of 5: Correlation between Binomial Coefficients and Probability)

Greatest Coefficient (2 of 5: Using the Ratio between Coefficients to find the greatest coefficient)

Greatest Coefficient (3 of 5: Defining the general term and choosing which is easier to use)

Greatest Coefficient (4 of 5: Finding the general ratio between the two coefficients and k)

Greatest Coefficient (5 of 5: Using the result to find the greatest term to find its coefficient)

Harder Greatest Coefficient (Finding greatest term given a defined variable)

Proving Binomial Identities (1 of 6: Reviewing and Proving the Symmetry Identity)

Proving Binomial Identities (2 of 6: Proving harder identities by substitution and using Theorem)

Proving Binomial Identities (3 of 6: Proving harder identities by comparing the constant term)

Proving Binomial Identities (4 of 6: Finding pairings for constant term & proving identity)

Proving Binomial Identities (5 of 6: Techniques to filter and find greatest absolute coefficient)

Proving Binomial Identities (6 of 6: Using Calculus to Prove Binomial Identities)

Proving Harder Binomial Identities (1 of 3: Deciphering identity to assist with proving)

Proving Harder Binomial Identities (2 of 3: Combining previous parts to find a relationship)

Proving Harder Binomial Identities (3 of 3: Finding a pattern in the expression and prove identity)

Overview of Permutations (1 of 4: Arranging n objects)

Overview of Permutations (2 of 4: Accounting for identical objects)

Overview of Permutations (3 of 4: Selective Arrangement)

Overview of Permutations (4 of 4: Connection to Binomial Coefficients)

Permutations and Combinations (1 of 2: Outline of the various expressions)

Arrangements and Counting Methods (1 of 4: Interpreting the question and finding conditions)

Permutations and Combinations (2 of 2: Applications towards probability and counting)

Arrangement and Counting Methods (3 of 4: Drawing an argument from symmetry)

Arrangements and Counting Methods (2 of 4: Solving an Arrangements question with Cases)

Arrangements and Counting Methods (4 of 4: Generating gaps to find probability)

Circular Arrangements (Outlining how to calculate arrangements around a circle)

Binomial Probability (1 of 2: What defines a Binomial Probability question)

Binomial Probability (2 of 2: Some Examples of Binomial Probability Questions)

Harder Circular Arrangements Questions (Worked Example of tricky questions with various conditions)

Harder Probability (Finding how many times it takes to increase the probability of an event)

Triangles Around a Circle (1 of 2: Problem Setup & Visualisation)

Paths Across a Grid (Permutations & Combinations)

Triangles Around a Circle (2 of 2: Two Convincing Arguments)

Binomial Probability: Dry & Rainy Days (Fixing a wrong textbook answer!)

Arranging 6 people in 4 rooms (Extension 2 Probability)

Single Pair in a Poker Hand (Extension 1 Probability)

Binomial Theorem Proof (2010 HSC question)

Red, Blue & White: Combinatorics HSC Question (1 of 2)

Red, Blue & White: Combinatorics HSC Question (2 of 2)

Arrangements: 10 Balls & 3 Boxes

Introduction to Binomial Theorem (1 of 3: Coefficients & Pascal's Triangle)

Introduction to Binomial Theorem (2 of 3: Basic Examples)

Introduction to Binomial Theorem (3 of 3: Choosing an order for the expansion)

Further Binomial Expansions (1 of 4: More Complicated Algebraic Combinations)

Further Binomial Expansions (2 of 4: General Term)

Further Binomial Expansions (3 of 4: Sigma Notation)

Further Binomial Expansions (4 of 4: Multiplying by a Trinomial)

Properties of Binomial Coefficients (1 of 2: Symmetry & Row Totals)

Properties of Binomial Coefficients (2 of 2: Pascal's Identity)

Factorial Notation (1 of 3: Comparison to other functions)

Factorial Notation (2 of 3: Formal definition)

Factorial Notation (3 of 3: Example questions)

nCr Notation (1 of 2: In terms of factorials)

nCr Notation (2 of 2: The mystery of the prime rows in Pascal's Triangle)

Manipulating Binomial Coefficients (1 of 2: Basic examples)

Manipulating Binomial Coefficients (2 of 2: Pascal's Identity)

Square Identity within Pascal's Triangle

General Term in a Binomial Expansion (1 of 2: Why is it useful?)

General Term in a Binomial Expansion (2 of 2: Harder example)

Locating a Specific Binomial Term (using general terms)

Y11 Maths Ext 1 Quiz (2 of 2: Binomial expansion, absolute value equation)

Find coefficient of x³ in a binomial expansion

Locating specific term in a complicated binomial expansion

General Term in a Binomial Expansion (1 of 2: Simplifying with index laws)

General Term in a Binomial Expansion (2 of 2: Using Tn to evaluate specific term)

Summing Coefficients of a Binomial Expansion

Binomial Theorem question: "Coefficient of x³ is double the coefficient of x²"

Greatest Binomial Coefficient (1 of 5: Review of prior theory)

Greatest Binomial Coefficient (2 of 5: Overview & introduction)

Greatest Binomial Coefficient (3 of 5: The general coefficient)

Greatest Binomial Coefficient (4 of 5: Expressing a useful ratio)

Greatest Binomial Coefficient (5 of 5: Locating & evaluating the coefficient)

Greatest Binomial Coefficient - worked example (1 of 2)

Greatest Binomial Coefficient - worked example (2 of 2)

Ordered Selections (1 of 3: Connection to probability trees)

Ordered Selections (2 of 3: Thinking through options)

Ordered Selections (3 of 3: Considering conditions)

Unordered Selections (1 of 3: Relation to permutations)

Unordered Selections (2 of 3: Relation to binomial theorem)

Unordered Selections (3 of 3: Applying to contexts)

Rearranging the word DECISIONS (1 of 2: Cases)

Rearranging the word DECISIONS (2 of 2: Symmetry & Gaps)

Navigating a Rectangular Grid (1 of 2: Unrestricted number of paths)

Navigating a Rectangular Grid (2 of 2: Solving with restrictions)

Pigeonhole Principle (2 of 2: Generalising the cases)

Pigeonhole Principle (1 of 2: Establishing a pattern)