`n` letters are written to n different persons and addresses on the n envelopes are also written. If the letters are placed in the envelopes at random, the probability that at least one letter is not placed in the right envelope, is (A) `1-1/n` (B) `1-1/(2n)` (C) `1-1/(n^2)` (D) `1-1/(n!)`

Options

A. `1/(1!) -1/(2!)+1/(3!)-1/(4!)+......(-1)^(n)1/(n!)`
B. `1/(2!)+1/(3!)+1/(4!)-1/(5!)+........1/(n!)`
C. `1/(2!)-1/(3!)+1/(4!)-1/(5!)+........(-1)^(n)1/(n!)`
D. None of these

Answer

C