Question

If there are $4$ addressed envelopes and $4$ letters. Then, the chance that all the letters are not mailed through proper enveloped is

• A. $1/24$
• B. $1$
• C. $23/24$
• D. $9/24$

Answer 1

Answer: (D)

$9/24$

Possible ways in which letter does not go to its box would by dearrangment formula that is

$=4!(1-\frac{1}{1!}+\frac{1}{2!}=\frac{1}{3!}+\frac{1}{4!})$

$=4!\left(\frac{9}{24}\right)$

and total possible ways $=4!$

$\therefore$ chance of going into incorrect box is,

$\Rightarrow \frac{4!\left(\frac{9}{24}\right)}{4!}=9/24$