Mixed permutation-combination problems combine both concepts. Select then arrange: First use C(n,r) to choose; then P(r,r) to arrange. Example: Select 3 from 5 and arrange = C(5,3) × 3! = 10 × 6 = 60 = P(5,3). Distribute distinct objects into groups: Use multinomial coefficient. Example: Arrange 10 people (5 type A, 3 type B, 2 type C) = 10!/(5! × 3! × 2!). Complex restrictions: Multiple conditions (e.g., at least 2 of type A, maximum 1 type B). Approach: Case-by-case counting or complementary method. Shortcut: Draw diagrams/tables for complex distributions. Exam tip: Break complex problems into independent steps. Verify using simple examples before finalizing.