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

Printable View

- Jun 17th 2013, 01:35 AMkashan123999Permutation 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 AMPlatoRe: Permutation Question
- Jun 17th 2013, 06:11 PMSorobanRe: 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 simplythe outcomes.*list*

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

There are**9***derangements*of the four letters:

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