AGES 10 - 15

Introduction to Counting and Probability

This class will teach students in grades 7-10 the foundations of counting and probability. Students will learn a variety of topics that expand beyond the regular school curriculum. Students will finish the course with an in-depth knowledge of permutations; combinations; probability; Pascal’s Triangle and the Binomial Theorem.

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Who is this course for
This Course is for Grade 5-Grade 9 Students who want to advance their knowledge in counting and probability.
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: Counting is Arithmetic
Counting by addition and multiplication, permutations
Chapter 2: Basic Counting Techniques
Count by cases, Complementary counting, constructive counting, counting with restrictions
Chapter 3: Correcting for Overcounting
Permutations with repeated elements, counting pairs and with symmetry
Chapter 4: Committees and Combinations
Combinations
Chapter 5: More with Combinations
Counting Paths on a grid, number of ways to form committee, distinguishability
Chapter 6: Some Harder Counting Problems
Solving advanced counting problems
Chapter 7: Introduction to Probability
Probability of equally likely outcomes, applications with counting techniques
Chapter 8: Basic Probability Techniques
Complementary probabilities, dependent event
Chapter 9: Think about it!
Learn faster approach to solve probability problems
Chapter 10: Geometric probability
Probability involving lengths and areas
Chapter 11: Expected Value
Definition and properties of expected value
Chapter 12: Pascal’s Triangle
Construction of Pascal’s triangle, relationship with combinatorics
Chapter 13: The hockey stick identity
Derivation of the hockey stick identity, and its application
Chapter 14: Binomial Theorem
Derivation and application of the binomial theorem
Chapter 15: More Challenging Problems
Hard problems in counting that use combinations of topics above
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