A derangement is a permutation where no element stays in its original position.
Example: 3 letters A, B, C in positions 1, 2, 3. Derangements: BCA, CAB. (A is not in position 1, B not in 2, C not in 3)
Total permutations: 3! = 6. Derangements: 2. So 1/3 of permutations are derangements here.
Derangements have a special formula. I'll show you next.