The Gateway to Computer Science Excellence
0 votes
847 views
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?
in Probability by (27 points)
reopened by | 847 views
0

1 Answer

+1 vote

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, $P = \frac{nD}{T} = \sum_{k = 0}^{n} \frac{(-1)^{k}}{k!}$

by Active (1.8k points)
+1

from sheldon ross.

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
50,737 questions
57,258 answers
198,087 comments
104,736 users