User talk:Kaushikbose09r

Using this recurrence, it can be shown that, in the limit,

\lim_{n\to\infty} {!n \over n!} = {1 \over e} \approx 0.3679\dots.

This is the limit of the probability pn = dn/n! that a randomly selected permutation is a derangement. The probability approaches this limit quite quickly.

More information about this calculation and the above limit may be found on the page on the statistics of random permutations.