Unordered selection and case counting

Practice combinations and constrained selection in this precalculus counting quiz. Work from identifying unordered groups to building committees, separating disjoint cases, and using complementary counts. Single-select and multiselect problems develop conceptual reasoning, efficient calculations, and error analysis with fully worked explanations. Each problem states whether roles or order matter. Attempt a solution before viewing the choices, then use the explanation to check your counting model and any exclusions. This extension practice prepares you for binomial coefficients and counting-based probability.