Source: Jaadu a.k.a Anshum Agarwal (Fourth Year, CSE, IITB and to be Tower Research Analyst) gave me this question. Said question from Tutorial of Prof. Sundar's course "Approximation Algorithms"
There are n letters and n envelopes. Your servant puts the letters randomly in the envelopes so that each letter is in one envelope and all envelopes have exactly one letter. (Effectively a random permutation of n numbers chosen uniformly). Calculate the expected number of envelopes with correct letter inside them.
Disclaimer: Not easy :P
Update (10/01/10): Solution: Posted by Giridhar (CSE, IITK alumnus and Yahoo! Sr. Software Engineer) in comments!! Nice solution.
Update (21/01/10): With the help of Asad Ali (EE, IITB Alumnus), a different solution posted by me in comments!!