Question

There are 5 letters and 5 different 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)

$44$

There are total $5!$ ways to arrange $5$ letters in $5$ envelopes.

Number of ways to put all the letters in wrong envelope is

$5![1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-\frac{1}{5!}]=44$