6. 7 dwarfs, each of different height. They stand in a random line, and shorter dwarfs behind taller ones are blocked from view. What is the expected number of dwarfs that Snow White can see when standing at the front of the line?
$\begin{array}{l}\text { 6. } 1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7} \text {. } \\ \text { Solution: } E_{n}=\frac{1}{n}\left(E_{n-1}+1\right)+\frac{n-1}{n} E_{n-1} \Rightarrow E_{n}=1+\cdots \\ +\frac{1}{n} \text {. }\end{array}$