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.

Counting by addition and multiplication, permutations

Count by cases, Complementary counting, constructive counting, counting with restrictions

Permutations with repeated elements, counting pairs and with symmetry

Combinations

Counting Paths on a grid, number of ways to form committee, distinguishability

Solving advanced counting problems

Probability of equally likely outcomes, applications with counting techniques

Complementary probabilities, dependent event

Learn faster approach to solve probability problems

Probability involving lengths and areas

Definition and properties of expected value

Construction of Pascal’s triangle, relationship with combinatorics

Derivation of the hockey stick identity, and its application

Derivation and application of the binomial theorem

Hard problems in counting that use combinations of topics above

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