Three letters, to each of which corresponds an envelope, are placed in the envelopes at random. The probability that all the letters are not placed in the right envelopes, is

Options

A. `(1)/(6)`
B. `(5)/(6)`
C. `(1)/(3)`
D. `(2)/(3)`

Answer

B

Explanation

Three letters can be placed in 3 evelopes in 3! Ways, whereas there is only one way of placing them in their right evelopes.
So, probablity that all the letters are placed in the right envelopes `=(1)/(3!)`
Hence, required probability `=1-(1)/(3!)+(5)/(6)`