# Permutation Question

• Jun 17th 2013, 01:35 AM
kashan123999
Permutation Question
A notorious postman delivered 4 letters to four houses in such a way that no house will get the correct letter.....in how many ways he delivered the letter??? please explain it please
• Jun 17th 2013, 02:00 AM
Plato
Re: Permutation Question
Quote:

Originally Posted by kashan123999
A notorious postman delivered 4 letters to four houses in such a way that no house will get the correct letter.....in how many ways he delivered the letter??? please explain it please

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• Jun 17th 2013, 06:11 PM
Soroban
Re: Permutation Question
Hello, kashan123999!

Quote:

A notorious postman delivered 4 letters to four houses in such a way that no house got the correct letter.
In how many ways could he have delivered the letter?

The simplest way is to simply list the outcomes.

Let the letters be $\displaystyle A,B,C,D.$

There are 9 derangements of the four letters:

. . $\displaystyle \begin{array}{c}BADC \\ CADB \\ DABC \end{array}\qquad\begin{array}{c} BDAC \\ CDAB \\ DCAB \end{array} \qquad \begin{array}{c} BCDA \\ CDBA \\ DCBA \end{array}$