 # Counting and Probability

To build on the concepts from the Introduction level course, students will build on their Counting and Probability knowledge. A thorough introduction for students in grades 7-10 to counting and probability topics such as permutations, combinations, Pascal's triangle, geometric probability, basic combinatorial identities, the Binomial Theorem, and more. Pigeonhole Principle Conditional Probability Graph Theory ##### Who is this course for
This course is for students who have completed our Introduction to Counting and Probability course.
This course typically takes 3-6 months to complete. This depends on the student's experience and how fast they can master the concepts and the knowledge. Our instructors move at the pace of the student, it may take extra time for some students to reinforce what they have learned.
##### Curriculum
###### Chapter 1: Review of Counting and Probability Basics Review of basic counting and probability, expected value, Pascal’s Triangle and Binomial Theorem, and the summation notation
###### Chapter 2: Sets and Logic Sets, logics, quantifiers
###### Chapter 3: A Piece of PIE Principle of Inclusion and Exclusion
###### Chapter 4: Constructive Counting and 1-1 correspondances Constructive counting, count by finding1-1 correspondances
###### Chapter 5: Pigeonhole Principle Pigeonhole Principle
###### Chapter 6: Constructive Expectation Linearity of Expectation
###### Chapter 7: Distributions Count the number of ways to place indistinguishable items into distinguishable boxes
###### Chapter 8: Mathematical Induction Induction
###### Chapter 9: Fibonacci Number Introduction and application for Fibonacci Numbers
###### Chapter 10: Recursion Recursion, Catalan Numbers
###### Chapter 11: Conditional Probability Conditional Probability, and their applications
###### Chapter 12: Combinatorial Identities Strategies of proving Combinatorial Identities
###### Chapter 13: Events with states State diagrams, random walks, events with infinite states
###### Chapter 14: Generating Functions Definition, and applications in deriving the binomial theorem, as well as formulas for distribution, partitions, and Fibonacci numbers
###### Chapter 15: Graph Theory Definitions, Basic Properties, Cycles and Paths, Planar Graphs, Eulerian and Hamiltonian paths
###### Chapter 16: Challenge Problems Hard problems in counting that use combinations of topics above

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