Question

There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.

Answer 1

There are 3 letters to be placed in 3 directed envelopes.

Total number of ways in which 3 letters can be placed in 3 envelopes $=3\times 2\times 1=6$

Number of ways in which only one letter can be placed in correct envelope = 3

Number of ways in which only 2 letter can be placed in correct envelopes = Number of ways in which all three is correct envelops = 1

So,

Total number of ways in which no letter in is correct envelop = 6 - (3 + 1) = 2

Required number of ways = 2