9. As shown in the figure, there are 6 network cables in parallel between points $A$ and $B$, with maximum information capacities of $1,1,2,2,3,4$ respectively. Now, any three cables are selected, and the maximum total information that can be transmitted from $A$ to $B$ is $x$. When $x>6$, the information flow is guaranteed to be smooth. Find the probability that the information flow is smooth.
$\begin{array}{l}\text { 9. } 1+1+4=1+2+3=6, \therefore P(x=6)=1+\frac{C_{2}^{1} C_{2}^{1}}{C_{6}^{3}}=\frac{1}{4} .1+2+4=2+2+3=7 \\ \therefore P(x=7)=\frac{5}{20}=\frac{1}{4} . 1+3+4=2+2+4=8, \therefore P(x=8)=\frac{3}{20} . \because 2+3+4=9 \\ \therefore P(x=9)=\frac{2}{20}=\frac{1}{10}, \therefore P(x \geqslant 6)=\frac{1}{4}+\frac{1}{4}+\frac{3}{20}+\frac{1}{10}=\frac{3}{4} .\end{array}$