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

Explanation

Total number of ways in which the letters can be put ` =3 ! =6`

Suppose, out of the three letters, one has been put in the correct envelope.

This can be done in `3_(C_1)`, i.e. 3, ways.

Now, out of three, if two letters have been put in the correct envelope, then the last one has been put in the correct envelope as well.

This can be done in `3_(C_3)`, i.e. one way.

therefore Number of ways `=3+1=4`

therefore Number of ways in which no letter is put in the correct envelope `=6-4=2`