The Probability of Derangement We have known that the number of derangemen t is N(AAA,.An)=N-S+S2-S3+.+(-1)Sk+.+(-I)”Sm wtere Nn d y) and the probabit y) ∴N(444A)=n-10 k=0 Sinethe difrence between the probabilty and e0.367879...is less than which means that the nl probabilit y is about 0.368,independen t of n,except for very small n.The Probability of Derangement probabilit y is about 0.368, independen t of , except for very small . , which means that the ! 1 and 0.367879...is less than , the difference between th e probabilit y ! ( 1) Since ! ( 1) ; and the probabilit y ! ( 1) ( ... ) ! ( 1,2,3,..., ) ! ! where !, and ( )! ( ... ) ... ( 1) ... ( 1) We have known that the number of derangemen t is 1 1 0 0 0 1 2 3 1 2 3 1 2 3 n n n e e k k k N A A A A n k n k n n k k n N n S N A A A A N S S S S S k k n k n k k k n k n n k k n  = − − −  = − = =         = = = − + − + + − + + − − −  = = =   ：