letter put in wrong envelop

juantheron · 2012-01-13 06:09:38

there are 6 letters and 6 dircted envelopes. then the number of ways in which all leters are put in wrong envelope is

bobbym · 2012-01-13 07:22:57

Hi;

juantheron · 2012-01-13 16:09:34

thanks bobbym but how can i get this recurrence relation

bobbym · 2012-01-13 16:25:02

Hi juantheron;

This is a standard derangement problem. Well known in combinatorics since Nicholas Bernoulli and Montmort both posed it and solved it. I did not invent this, I just had to look it up. Euler is the one who came up with that recurrence. Whole books have been written about this type problem. The first derivation starts from the principle of inclusion - exclusion. Take a look here to see what I mean:

http://en.wikipedia.org/wiki/Derangement

In combinatorics we solve problems by reducing them to one of several major classes. Birthday problems, urn problems, coupon collector problems, derangement problems etc. Here I just had to look up the type of problem and use the formula provided. Remember, research is part of solving the problem.

juantheron · 2012-01-14 01:16:02

Thanks bobbym for nice link

bobbym · 2012-01-14 01:27:27

Hi juantheron;

You are welcome. That generally covers most of it.

Math Is Fun Forum

#1 2012-01-13 06:09:38

letter put in wrong envelop

#2 2012-01-13 07:22:57

Re: letter put in wrong envelop

#3 2012-01-13 16:09:34

Re: letter put in wrong envelop

#4 2012-01-13 16:25:02

Re: letter put in wrong envelop

#5 2012-01-14 01:16:02

Re: letter put in wrong envelop

#6 2012-01-14 01:27:27

Re: letter put in wrong envelop

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