Q. The number of ways can 10 letters be placed in 10 marked envelopes, so that no letter is in the right envelope are
A) $10!\left( 1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + ... + \frac{1}{10!} \right)$
B) $10!\left( 1 + \frac{1}{1!} - \frac{1}{2!} + \frac{1}{3!} - ... - \frac{1}{10!} \right)$
C) $\left\{ 1 + \frac{1}{1!} - \frac{1}{2!} + \frac{1}{3!} - ... - \frac{1}{10!} \right\}$
D) $9!\left\{ 1 + \frac{1}{1!} - \frac{1}{2!} + \frac{1}{3!} - ... - \frac{1}{10!} \right\}$
Explanation
(a)
The required number of ways is equal to the number of dearrangements of 10 objects.
$\therefore$ Required number of ways
$= 10!\left\{ 1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + ... + \frac{1}{10!} \right\}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.