Permutations with special conditions handle repetitions and restrictions. Circular permutations: Objects arranged in circle. Formula: (n-1)! (fix one position to eliminate rotations). Beads/bracelet: (n-1)!/2 (account for flipping). Permutations with repetition: n^r (each of r positions can have n choices). Example: 3-digit numbers from 1-5 with repetition = 5³ = 125. Restricted positions: Some objects must/cannot be adjacent. Approach: (1) Fix restricted objects; (2) Arrange remaining; (3) Multiply. Example: ABCD where A,B must be adjacent. Treat AB as one unit: 3! × 2! = 12 (internal arrangement of AB). Exam tip: Identify restriction type clearly. Read problem carefully for 'adjacent', 'separate', 'not adjacent'.