my uncle wrote three different letters and addressed three envelopes. then he went outside for a walk. while he was out, his little daughter

Hi Rosala,

here all possibilities:

I. 

    Letter 1 put into envelope 1

    Letter 2 put into envelope 2              or          Letter 2 put into envelope 3

    Letter 3 must be in envelope 3                       Letter 3 must be in envelope 2

    we have:

                       1. Letter 1 in envelope 1

                           Letter 2 in envelope 2

                           Letter 3 in envelope 3

                        2. Letter 1 in envelope 1

                            Letter 2 in envelope 3

                            Letter 3 in envelope 2

we can change places 3 times. Letter 1 can start in envelope 1 or in envelope 2 or in envelope 3

so we have 2 * 3 = 6

my uncle wrote three different letters and addressed three envelopes. then he went outside for a walk. while he was out, his little daughter put a letter into each envelope and sealed it. what is the probability that none of the letters was in the correct envelope?

$$\small{\text{
\textcolor[rgb]{0,1,0}{okay} \text{ \textcolor[rgb]{1,0,0}{false}
\begin{array}{|l|c|c|c|}
\hline
$n& letter 1 & letter 2 & letter 3 $ \\
\hline
$1& envelope\ \textcolor[rgb]{0,1,0}{1} & envelope\ \textcolor[rgb]{0,1,0}{2} & envelope\ \textcolor[rgb]{0,1,0}{3} $ \\
$2& envelope\ \textcolor[rgb]{0,1,0}{1} & envelope\ \textcolor[rgb]{1,0,0}{3} & envelope\ \textcolor[rgb]{1,0,0}{2} $ \\
$3& envelope\ \textcolor[rgb]{1,0,0}{2} & envelope\ \textcolor[rgb]{1,0,0}{1} & envelope\ \textcolor[rgb]{0,1,0}{3} $ \\
$\textcolor[rgb]{1,0,0}{4}& envelope\ \textcolor[rgb]{1,0,0}{2} & envelope\ \textcolor[rgb]{1,0,0}{3} & envelope\ \textcolor[rgb]{1,0,0}{1} $ \\
$\textcolor[rgb]{1,0,0}{5}& envelope\ \textcolor[rgb]{1,0,0}{3} & envelope\ \textcolor[rgb]{1,0,0}{1} & envelope\ \textcolor[rgb]{1,0,0}{2} $ \\
$6& envelope\ \textcolor[rgb]{1,0,0}{3} & envelope\ \textcolor[rgb]{0,1,0}{2} & envelope\ \textcolor[rgb]{1,0,0}{1} $ \\
\hline
\end{array}
}}$$

The probability that none of the letters was in the correct envelope is  $$\frac{2}{6} = \frac{1}{3} = 33.\overline{3}\ \%$$

heureka....i dont understand you answer...i tried solving this but i couldnt.....can u explain your answer to me please!

Hi Rosala,

There are 6 different possibilities to put 3 letters into 3 envelopes. I have numbered serially them with from 1 to 6. Then I have looked which letters agree with which envelopes. There remain 2 possibilities in those all 3 letters in the envelopes are wrong franked. Then the probability is: 2/6

how come 6, it said ' what is the probability that none of the letters was in the correct envelope'  , there are 3 letters and 3 envelopes so it should be 9.......im sooo confused Heureka!

Hi Rosala,

for example if Letter 1 is in envelope 1 then you can't put Letter 2 or Letter 3 into envelope 1.

hi heaureka,...so now i understood why not 9 ...but would you mind telling me why6?im just so confused thats why!thanks!

Thanks Heureka  

And thanks for the good questions Rosala.    

Thanks Melody and Heureka!

Thank you Heureka for all the hard work for me!i really appreciate it!thanks!