The names of 8 students are listed randomly. What is the probability that Al, Bob, and Charlie are all in the top 4? My attempt at a solution: There are $C_{4,3}$ ways to arrange Al, Bob, and Charlie in the top 4, and $C_{5,4}$ ways to arrange the other 5 people. All of this is over $C_{8,4}$, giving $$\frac{C_{4,3}C_{5,4}}{C_{8,4}}=\frac{2}{7}$$ Is this correct?

$4$ slots are up for grabs, so a simple way is to just  compute $\dfrac48\cdot\dfrac37\cdot\dfrac26= \dfrac{1}{14}$
