Eight persons are to be transported from city A to city B in three...

Let us find the different ways so that $8$ persons can travel in $3$ cars.

$\begin{cases}{C}_{1} & {C}_{2} & {C}_{3} \\ 3 & 3 & 2 \\ 2 & 3 & 3 \\ 3 & 2 & 3\end{cases}$

Hence we have $3$ ways.

Now the number of ways to distribute $8$ persons such that they can travel in $3$ cars with any car carrying maximum of $3$ persons is \left(\dfrac{8 !}{3 ! 3 ! 2 !}\right) \times 3$</p><p>$= 1680$</p><p>Therefore, the required answer is$1680