# Nothing is in its place!!!

Level pending

Consider a set of a large number of pairs of envelopes and letters. The $$n^{th}$$ envelope and letter is denoted by $$E_{n}$$ and $$L_{n}$$ respectively and both of them have the number $$n$$ printed on them.
All the letters have been taken out of the envelopes and now are arranged randomly.

Find the probability that the letter $$L_{n}$$ does not go in envelope $$E_{n}$$ $$\forall n \in \mathbb{N}$$

Details and Assumptions:
By a large number, I mean the total number of pairs approach infinity.

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