Having some trouble with this combinatorics problem


by Calabi_Yau
Tags: combinatorics, trouble
Calabi_Yau
Calabi_Yau is offline
#1
Nov19-12, 02:19 PM
P: 29
6 friends go to a party, each one carrying a different umbrella. They place the umbrellas outside. When the party is over, they are drunk and each one grabs an umbrella at random.
In how many ways could none of them have taken the right umbrella?

I'm having a bit trouble with this, as I can't seem to solve it without having to do some rough counting some times. Can any of you bother to solve this and explain it to me?
Phys.Org News Partner Mathematics news on Phys.org
Researchers help Boston Marathon organizers plan for 2014 race
'Math detective' analyzes odds for suspicious lottery wins
Pseudo-mathematics and financial charlatanism
Robert1986
Robert1986 is offline
#2
Nov19-12, 06:34 PM
P: 828
Take a look at this link: http://www.proofwiki.org/wiki/Hat-Check_Problem
Norwegian
Norwegian is offline
#3
Nov19-12, 07:23 PM
P: 144
You are asking about the number of derangments Sn of a set with n elements. If you are looking for an exact answer, you can either use the recurrence relation Sn+1=n(Sn+Sn-1), or compute the alternating sum Ʃ(-1)in!/i! where i goes from 0 to n.

Calabi_Yau
Calabi_Yau is offline
#4
Nov20-12, 09:58 AM
P: 29

Having some trouble with this combinatorics problem


Thanks guys.


Register to reply

Related Discussions
combinatorics problem General Math 14
A combinatorics Problem Set Theory, Logic, Probability, Statistics 0
A combinatorics Problem Precalculus Mathematics Homework 1
Combinatorics Problem Precalculus Mathematics Homework 3
Combinatorics problem Precalculus Mathematics Homework 3