What is probability that 5 letters can not put in to the right envelope?

Solution (By Examveda Team)

This is the most general question on the derangement principle that is often asked in the examinations.
If n particular items need to be arranged or organized in a row in such a manner that none of them acquires its usual or correct place is calculated using the formula:
No. of way in which they are can't put correctly,
= n! [1- (1/1!) + (1/2!) - (1/(3!) + (1/4!) + ..............]
= 5! [1 - (1/1!) + (1/2!) - (1/3!) + (1/4!) - (1/5!)]
= 120 * [1/2 - 1/6 + 1/24 - 1/120]
= 44 ways.
And,
5 letters can be placed correctly in 5! ways.
So, required probability would be,
= 44/5! = 44/120 = 11/30.