Question

There are $5$ letters and $5$ directed envelopes.The number of ways in which all the letters can be put in wrong envelope is

• A. $119$
• B. $44$
• C. $59$
• D. $40$

Answer 1

Answer: (B)

$44$

$5$ letters $5$ directed envelope

All the of letters Put wrong wrong :

Number of ways =

$=[1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-\frac{1}{5!}]5!=[1-1+\frac{1}{2}-\frac{1}{6}+\frac{1}{24}-\frac{1}{120}]5!=[\frac{2}{6}+\frac{4}{120}]5!=[\frac{1}{3}+\frac{1}{30}]5!=\left[\frac{11}{30}\right]120=44$