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PERMUTATIONS AND COMBINATIONS

Home > My Courses > HSC Year 11 Mathematics Extension 1 – Combinatorics > PERMUTATIONS AND COMBINATIONS
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HSC Year 11 Mathematics Extension 1 - Combinatorics

PERMUTATIONS AND COMBINATIONS
Product Principle
  • Video – Counting Techniques with Repetitions (10:14)
  • Video – Counting Techniques with Repetitions of Mixed Cases (5:36)
  • Video – Counting Techniques without Repetitions (6:48)
  • Video – Arrangements with Repetitions: Combination Locks (1:35)
  • Video – Arrangements with Repetitions: Lights On/Off (1:54)
  • Video – Arrangements with Repetitions: Binary Numbers (1:46)
  • Video – Arrangements without Repetitions: Numeric Passwords (3:06)
  • Video – Arrangements without Repetitions: Alphanumeric Passwords (2:14)
  • Video – Arrangements without Repetitions: Combination Locks (1:25)
Factorials
  • Video – Definition of Factorial (5:52)
  • Video – Simplifying Expressions involving Factorials (4:22)
  • Video – Equations involving Factorials (2:08)
  • Video – Arrangements of 4 Cards (2:04)
  • Video – Arrangements of 9 People Queuing Up a Line (5:18)
  • Video – Arrangements of 6 Girls and 2 Boys (4:09)
  • Video – Formula of Considering Duplicates (2:57)
  • Video – Arrangements involving Duplicates (3:01)
  • Video – Arrangements involving Duplicates in Groups (1:11)
  • Topic – Calculating Factorials
  • Topic – Calculating Factorials involving Fractions
  • Topic – Factorials involving Multi Factorials & Fractions
Permutations
  • Video – Ordered Selections (4:45)
  • Video – Ordered Selections without or with Replacement (2:38)
  • Video – Definition of Permutation (2:57)
  • Video – Calculating Permutations (2:23)
  • Video – Equations involving Permutation (1:20)
  • Video – Introduction to Permutation (4:34)
  • Video – Applying Permutations (2:49)
Permutations Involving Restrictions
  • Video – Arrangements Concerning Repetitions (4:13)
  • Video – Unknown Number of Permutations (1:16)
  • Video – Arrangements of Numeric Digits Less Than a Certain Number (3:15)
Arrangements in a Circle
  • Video – Understanding Arrangements in a Round Table (3:51)
  • Video – Arrangements in a Round Table (2:49)
  • Video – Arrangements in a Necklace (1:59)
  • Video – Permutations in a Round Table (3:06)
  • Video – Permutations in a Necklace (1:38)
Combinations
  • Video – Counting Techniques without Replacements (2:28)
  • Video – Unordered Selections: Choosing Letters (8:21)
  • Video – Unordered Selections: Forming Groups (3:02)
  • Video – Definition of Combination (3:59)
  • Video – Simplifying Combinations (3:25)
  • Video – Equations involving Combination (3:46)
  • Video – Proofs involving Combination (3:30)
  • Video – Understanding Combination (1:49)
  • Video – Choosing Combinations from Two Groups (4:17)
  • Video – Combinations involving At Least (2:26)
  • Video – Combinations involving Duplicates (5:05)
Applications of Counting Techniques
  • Video – Majority Decision (4:11)
  • Video – Selection & Arrangement of Words involving Same Letters (3:50)
  • Video – Select & Arrangement of Words involving Vowels & Consonants (1:40)
  • Video – Select & Arrangement of Books in Two Groups (1:42)
Pigeon-Hole Principle
  • Topic – Pigeon-Hole Principle 1
  • Topic – Pigeon-Hole Principle 2
Probabilities using Combinations
  • Video – Combinations involving Probability (4:06)
  • Topic – Probability involving Combinations: Single Events
  • Topic – Probability involving Combinations: Exactly in 2 Groups
  • Topic – Probability involving Combinations: Not More Than in 2 Groups
BINOMIAL THEOREM
Binomial Expansions
  • Video – Binomial Expansion using Pascal’s Triangle (10:43)
  • Video – Basic Binomial Expansion (2:27)
Extension of Binomial Expansions to Fractions and Negative Indices
  • Video – Binomial Expansion of Subtractions (2:45)
  • Video – Binomial Expansion involving Coefficients (2:27)
  • Video – Binomial Expansion involving Fractions (2:03)
  • Video – Binomial Expansion involving Non-Linear Terms (2:15)
Binomial Coefficient
  • Video – Binomial Expansion using Combination Coefficients (13:29)
  • Video – Specific Terms of Binomial Expansion (4:39)
  • Video – Coefficients of Binomial Terms (1:43)
  • Video – General Term of Binomial Expansions (6:19)
  • Video – Binomial Expansion: Sigma Notation (5:57)
  • Video – Binomial Expansion: Finding the Term (3:53)
  • Video – Binomial Expansion: Finding the Coefficient (2:44)
  • Video – Finding Coefficients of Binomial Expansions involving Rational Terms (2:50)
  • Video – Finding Coefficients of Binomial Expansions with Two Pronumerals (2:05)
  • Video – Binomial Expansion: Term Independent of x (5:52)
General Binomial Theorem
  • Video – Binomial Expansion: Finding the Coefficients (7:14)
  • Video – Binomial Expansion: Finding the Coefficients involving Fractions (6:20)
  • Video – Proof involving Binomial Expansions (6:39)
  • Video – Simplifying Binomial Series by Substituting Values (5:58)
  • Video – Simplifying Binomial Series by Differentiations (4:00)
  • Video – Simplifying Binomial Series by Integrations (7:30)
Application of Binomial Expansions
  • Video – Binomial Expansion: Ratio of Consecutive Terms Theory (6:10)
  • Video – Binomial Expansion: Ratio of Consecutive Terms (3:47)
  • Video – Binomial Expansion: Ratio of Consecutive Terms involving Negative Signs (3:38)
  • Video – Binomial Expansion: Single Greatest Coefficient (8:01)
  • Video – Binomial Expansion: Two Greatest Coefficients (5:29)
  • Video – Binomial Expansion: Single Numerically Greatest Coefficient (5:50)
  • Video – Binomial Expansion: Two Numerically Greatest Coefficients (6:02)
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