Derangement U=Sn A;={π|π()=} A虹={π|i∈I,π(2)=}Ar=(n-|I)！ ∩A-(-1)川A iEln] ICIn] = (-1)川(m-I0！=】 -（份）- IC[n] n. k！ ≈ o =0Derangement Ai = {￾ | ￾(i) = i} AI = {￾ | ⇥i ￾ I, ￾(i) = i} |AI | = (n ￾ |I|)! = ￾ I￾[n] (￾1)|I| (n ￾ |I|)! = ⇤ n k=0 (￾1)k ￾n k ⇥ (n ￾ k)! = n! ￾ n k=0 (￾1)k k! ￾ n! e ￾ I￾[n] (￾1)|I| |AI | ￾ ￾ ￾ ￾ ￾ ￾ ￾ i￾[n] Ai ￾ ￾ ￾ ￾ ￾ ￾ = U = Sn