Systematically count finite outcomes using organized lists, tables, and tree diagrams, applying the fundamental counting principle, addition and multiplication principles, permutations with or without repetition, and combinations while distinguishing ordered arrangements from unordered selections. Apply the binomial theorem for nonnegative integer powers, expanding $(a+b)^n$, identifying terms and coefficients, and interpreting binomial coefficients as combination counts. Calculate probabilities in equally likely finite sample spaces using counting techniques, conditional probabilities, and complementary events, and determine whether events are independent or mutually exclusive using multiplication and conditional-probability rules.