Question

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

• A. $1/24$
• B. $11/24$
• C. $5/8$
• D. $23/24$

Answer 1

The correct option is D $23/24$

Required probability
$=1-P$ (all the letters are put in correct envelops)
The number of ways of putting the letters in the envelops ${=}^4{P}_4=4!$
The number of ways of putting letters in correct envelops $=1$
$\therefore$ Required probability $=1-\frac{1}{24}=\frac{23}{24}$.