{"id":37284,"date":"2026-04-21T15:10:36","date_gmt":"2026-04-21T07:10:36","guid":{"rendered":"https:\/\/blog-admin.thethinkacademy.com\/?p=37284"},"modified":"2026-06-25T21:24:57","modified_gmt":"2026-06-25T13:24:57","slug":"amc8-counting-and-probability","status":"publish","type":"post","link":"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/04\/21\/amc8-counting-and-probability\/","title":{"rendered":"Mastering Counting and Probability for AMC 8: Key Rules and Real Problems"},"content":{"rendered":"\n

Introduction<\/h2>\n\n\n\n

AMC 8<\/a> Counting and Probability is a major topic in the contest and often challenges students who are not yet confident with formulas. These questions include everything from basic counting principles to advanced probability word problems and permutations and combinations. In this guide, we explain the essential rules, show how they work, and highlight AMC 8 past problems that demonstrate each formula. Practicing with worksheets and real contest examples will help students strengthen their problem-solving skills.<\/p>\n\n\n\n

This article focuses on AMC 8 Counting and Probability<\/strong>. For a full study plan, also check out our guides on AMC 8 Algebra Formulas<\/a> and AMC 8 Geometry Formula<\/a>. For a complete overview of the AMC 8 competition including format, scoring, and registration for Canadian students, see our AMC 8 Math Competition: The Complete Guide for Canadian Students<\/a>!<\/p>\n\n\n

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\"\"<\/a><\/figure>\n<\/div>\n\n\n
Rule or formula<\/th>When to use it<\/th>AMC 8 example year<\/th><\/tr><\/thead>
Sum rule<\/td>Counting mutually exclusive cases<\/td>2015 Problem 4<\/td><\/tr>
Product rule<\/td>Counting independent sequential steps<\/td>2019 Problem 14<\/td><\/tr>
Basic probability<\/td>Finding likelihood of a single event<\/td>2014 Problem 16<\/td><\/tr>
Permutations<\/td>Ordered arrangements with restrictions<\/td>2018 Problem 16<\/td><\/tr>
Combinations<\/td>Unordered selections from a group<\/td>2018 Problem 16<\/td><\/tr>
Complementary counting<\/td>Subtracting unwanted outcomes from total<\/td>Various<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

The Sum Rule: When to Add in AMC 8 Counting Problems<\/h2>\n\n\n\n
\"AMC<\/figure>\n\n\n\n

AMC 8 Example (2015, Problem 4)<\/strong> – applying the sum rule<\/h3>\n\n\n\n
\"AMC<\/figure>\n\n\n\n

The Centerville Middle School chess team has 2 boys and 3 girls. A photographer wants them in a row with a boy at each end and the girls in the middle.<\/p>\n\n\n\n