Question

A person write 4 letters and addresses 4 envelopes. If the letters are placed in the envelopes at random, then the probability that all letters are not placed in the right envelopes, is

• A. $\frac{1}{4}$
• B. $\frac{11}{24}$
• C. $\frac{15}{24}$
• D. $\frac{23}{24}$

Answer 1

The correct option is D

$\frac{23}{24}$

Total number of ways of placing four letters in 4 envelops = 4! = 24

All the letters can be dispatched in the right envelops in only one way, Therefore, the probability that all the letters are placed

In the right envelops is $\frac{1}{24}$

Hence, probability that all the letters are

not placed in the right envelops $=1-\frac{1}{24}=\frac{23}{24}$