0 votes 0 votes Suppose that each of N men at a party throws his hat into the center of the room. The hats are first mixed up, and then each man randomly selects a hat. What is the probability that none of the men selects his own hat? Probability probability engineering-mathematics + – mk_15 asked Jun 4, 2016 reopened Nov 4, 2018 by Mk Utkarsh mk_15 2.9k views answer comment Share Follow See 1 comment See all 1 1 comment reply Mk Utkarsh commented Nov 4, 2018 reply Follow Share Similar question https://gateoverflow.in/261274/at-least-one-person-receives-his-her-own-hat 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes There is a concept called Derangement. Using that, Number of ways in which N men can be deranged with n hats(say $nD$) = $n! \sum_{k = 0}^{n} \frac{(-1)^{k}}{k!}$ Total number of ways in which n men can pick hats(say $T$) = $n!$ Therefore, $P = \frac{nD}{T} = \sum_{k = 0}^{n} \frac{(-1)^{k}}{k!}$ Pranav Kant Gaur answered Jun 6, 2016 Pranav Kant Gaur comment Share Follow See 1 comment See all 1 1 comment reply Sachin Mittal 1 commented Jan 3, 2017 reply Follow Share from sheldon ross. 1 votes 1 votes Please log in or register to add a comment.