Question

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

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

Answer 1

Answer: (A)

$\frac{1}{4}$

Given that a person writes four letter and address four envelopes then,

Number of ways in which four letter can be placed in four envelopes is $4!=24$ ways

Now, if all the letters go into the right envelopes then that can be done only in $1$ way.

$\therefore$ The probability that the letters go into the right envelop$=\frac{1}{24}$

$\therefore$ the probability that one go into the right envelops is $1-\frac{1}{24}=\frac{23}{24}$

Hence the required probability is $\frac{23}{24}$.