Basic Counting-Starting to Count
Companion e-book
Why Counting
Rule of Sum
How Not to Use the Rule of Sum
Convenient Language: Sets
Generalized Rule of Sum
Basic Counting-Recursive Counting
Number of Paths
Rule of Product
Back to Recursive Counting
Basic Counting-Tuples and Permutations
Number of Tuples
Licence Plates
Tuples with Restrictions
Permutations
Binomial Coefficients-Combinations
Previously on Combinatorics
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Generating Combinatorial Objects: Code
Number of Games in a Tournament
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Combinations
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Slides
Binomial Coefficients-Pascal's Triangle
Pascal's Triangle
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Symmetries
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Row Sums
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Binomial Theorem
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Slides
Binomial Coefficients-Practice Counting
Practice Counting
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Slides
Advanced Counting-Combinations with Repetitions
Review
Salads
Combinations with Repetitions
Advanced Counting-Problems in Combinatorics
Distributing Assignments
Distributing Candies Among Kids
Counting Credit Card PINs
Splitting into Working Groups
Probability-What is Probability?
The Paradox of Probability Theory
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Galton Board
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Natural Sciences and Mathematics
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Rolling Dice
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More Probability Spaces
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Slides
Probability-Probability: Do's and Don't's
Not Equiprobable Outcomes
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More About Finite Spaces
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Mathematics for Prisoners
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Not All Questions Make Sense
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Slides
Probability-Conditional Probability
What Is Conditional Probability?
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How Reliable Is The Test?
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Bayes' Theorem
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Conditional Probability: A Paradox
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Past and Future
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Independence
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Slides
Probability-Monty Hall Paradox
Monty Hall Paradox
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`Our Position'
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Slides
Random Variables-Random Variables and Expectations
Random Variables
Average
Expectation
Random Variables-Linearity of Expectation
Linearity of Expectation
Birthday Problem
Random Variables-Expectation is Not All
Expectation is Not All
Random Variables-Markov’s Inequality
From Expectation to Probability
Markov’s Inequality
Project: Dice Games-Dice Game Problem
Dice Game Problem
Project: Dice Games-Project Description
Optimal Strategy