Combinatorics Pages

• An Introduction to Counting via Computing
  • The importance of connecting counting processes and sets of outcomes
• Addition and Subtraction Principles
  • Addition Principle
  • Subtraction Principle
• The Multiplication Principle
  • Multiplication Principle (MP)
  • Cartesian Product Problems
  • Cartesian Products with copies of the same set
  • Why Independence Matters
  • Applying the MP to other types of problems
• Coordinating Fundamentals of Counting Problems
  • New Functions for Counting
  • Example Problem 0:
  • Example Problem 1:
  • Example Problem 2:
  • Example Problem 3:
  • Encoding Outcomes
  • Practice Problems:
  • End of Essay
• Combinatorics - Four Basic Problem Types
  • Type 1 Problems (Arrangement with repetition)
  • Type 2 Problems (Arrangement without repetition)
  • Type 3 Problems (Selection without repetition)
  • Type 4 Problems (Selection with repetition)
  • Differences between Type 1 and Type 2
  • Differences between Type 2 and Type 3
  • Differences between Type 3 and Type 4
• Type 1 - Arrangement with Repetition
  • Active Code 1
  • Quick Check 1.1
  • Quick Check 1.2
  • Quick Check 2.1
  • Quick Check 3.1
  • Quick Check 3.2
  • Quick Check 3.3
  • Active Code
  • Quick Check 4.1
  • Quick Check 5.1
  • Active Code 4
  • General formula for Arrangements with Repetition
  • Active Code 5
  • Quick Check 8.1
• Type 2 - Arrangement without Repetition - Permutations
  • Active Code
  • Active Code
  • Active Code
  • Quick Check 1.1
  • General formula for Arrangements without Repetition of all \(n\) elements
  • General Formula for Arrangements without Repetition
• Type 3 - Selection Without Repetition - Combinations
  • Active Code 1
  • Quick Check 1.1
  • General formula for Selection without Repetition
  • Combinations as Sums of Sums
  • Active Code 2
  • Active Code 3
  • Some Practice Problems
  • Active Code 4
  • Active Code 5
• Type 4 - Selection With Repetition
  • Quick Check 1
  • Quick Check 2
• The ABCDEs of Counting
  • Problem 1:
  • Problem 2:
  • Problem 3:
  • Problem 4:

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