Eight persons are to be transported from city A to city B in three cars of different makes. If each car can…

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

$\begin{array}{ccc}{C}_1& C_2& C_3\\ 3& 3& 2\\ 2& 3& 3\\ 3& 2& 3\end{array}$

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 $\left(\frac{8!}{3!3!2!}\right)\times 3$

$=1680$

Therefore, the required answer is $1680$