Introduction to Counting and Probability

Curriculum details

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This course may be taken optionally once Introduction to Algebra is completed. Art of Problem Solving recommends taking it just before Introduction to Geometry (normally scheduled in tenth grade). If you choose to take Introduction to Counting and Probability, you can delay Introduction to Geometry as needed to complete this course first.

This textbook covers the material in greater depth than a traditional high school course, and includes many challenging problems. For this reason, we recommend that you take things as slowly as the student needs and err on the side of completing a small number of problems with full understanding and without overwhelming the student. Aim to spend between thirty minutes and an hour per day five days a week on this book.

Start each new section by watching the free videos for the relevant section at artofproblemsolving.com/videos/counting. Then, go over the example problems at the beginning of each section. Finally, have the student work through the problems at the end of the section in the textbook (there is no workbook).

Be aware that the textbook includes problems of a wide range of difficulty, and the majority of students (and parents!) are not expected to solve the most challenging ones without help. Use the solutions manual to work through any missed problems together. You may opt to skip the "Challenge" sections and complete only the regular problems if desired.

For students who would like to go more in depth or prefer a live class format, Art of Problem Solving also offers challenging, instructor-led online classes at artofproblemsolving.com/school.