Derangement - the !n formula through recurrence, and Euler's Constant e comes in

A derangement is a permutation of the elements of a set, such that no element appears in its original position. We derive the formula using the recurrence relation.

00:00:00 Introduction of Derangement, sub-factorial !n
00:00:50 An example - letters and envelopes - every letter is mis-placed
00:02:33 Another example for D_4.
00:04:28 For bigger n, we resort to recurrence
00:10:20 The equation for the recurrence relation
00:12:20 Derive the formula for !n from the recurrence relation using telescoping
00:17:50 The present of Euler's number e in the formula
00:22:06 Validation of the first few !n vs n!/e

We will introduce the derivation of the formula through Inclusion Exclusion Principle.
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[sumittete]

29:40, why did you add 1/2 in the floor function? Please explain

[RahulMani]

22:59, D8 should be rounded up as D4, D6 and D10, etc to 14833 ??