So I was reading up about the derangement recurrence relation proven in a combinatorical way. The proof I was looking at is at this webpage. The combinatorical proof is at the bottom of the page below the algebraic proofs. "ttp://planetmath.org/?op=getobj&from=objects&id=11991"[/URL] So in this proof the part I'm not understanding is:[QUOTE]Adding n before any of the n−1 elements of produces a derangement of [n] .[/QUOTE] It seems to me this doesn't always lead to a derangement of [n]. Such in the case of (2, 1, 5, 4, 3). If you add 6 before 2 then you get (6, 2, 1, 5, 4, 3), which is no longer a derangement. What am I missing that I'm not understanding this?