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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)

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

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)

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)

General Binomial Theorem

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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