A person writes $4$ letters and addresses $4$ envelopes. If the letters are placed in the envelopes at random, the probability that not all letters are placed in correct envelopes is 

Required probability $= 1 - P$(all the letters are put in correct envelopes)

The number of ways of putting the letters in the envelopes ${=}^4{P}_4=4!$

The number of ways of putting all the letters in correct envelopes $= 1$ 

$\therefore$Required probability $=1-\frac{1}{24}=\frac{23}{24}.$