2 votes 2 votes 4 person wearing different hat went to restaurant, they gave there hat to manager, manager has habit of forgetting thing while returning manager gave hat back to each person, probability that none of the person gets there respective hats is ? Probability iiith-pgee probability + – Tesla! asked Apr 21, 2018 Tesla! 1.0k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
8 votes 8 votes Total Number of ways 4 hats can be arranged/distributed = 4!=24 Number of degeneration of four numbers will give number of arrangements where no one gets correct hat. $4!/2! - 4!/3! +4!/4! $ $=24/2 - 24/6 +1$ $=12-4+1$ $9$ Probability that no one gets correct hat=$9/24$=.375 rahul sharma 5 answered Apr 21, 2018 • edited Apr 21, 2018 by rahul sharma 5 rahul sharma 5 comment Share Follow See all 6 Comments See all 6 6 Comments reply Tesla! commented Apr 21, 2018 reply Follow Share Probability 9? 0 votes 0 votes rahul sharma 5 commented Apr 21, 2018 reply Follow Share Sorry.I read the question wrongly.I have updated now.Please check 0 votes 0 votes Akhilesh Singla commented Apr 22, 2018 reply Follow Share I tried $P(\bar{A} \cap \bar{B} \cap \bar{C} \cap \bar{D}) = 1- P(A\cup B \cup C \cup D)$ But I was getting wrong answer. Why is this approach incorrect? I have had solved exactly same problem with three hats using this approach. Also, could you please provide a good link to study degeneration? 0 votes 0 votes rahul sharma 5 commented Apr 22, 2018 reply Follow Share I studied it some time during Gate preparation. You can Google.it's a common topic. I applied the same approach as you mentioned. May be you did some calculation mistake 0 votes 0 votes sonveer tomar 1 commented Apr 24, 2018 reply Follow Share We can solve like by enumerating all 24 case, and counting the one where none gets there hats. 0 votes 0 votes Akhilesh Singla commented Apr 24, 2018 reply Follow Share I am unable to find a meaningful link with search term "degeneration of numbers". 0 votes 0 votes Please log in or register to add a comment.
4 votes 4 votes using dearrangements aditi19 answered Aug 12, 2018 aditi19 comment Share Follow See all 0 reply Please log in or register to add a comment.