In how many ways can they travel by these cars so as to reach in time An cricket team with eleven players,the team manager,the physiotherapist and two umpires are to travel from the hotel where they are staying to the stadium where the test match is to be played.Four of them residing in the same town own cars,each a four seater which they will drive themselves.The bus which was to pick them up failed to arrive in time after leaving the opposite team at the stadium.In how many ways can they travel by these cars so as to reach in time,if the seating arrangement in each car is immaterial and all the cars reach the stadium by the same route. * * * If the four car-owning persons drive their respective cars,then they have $3$ vacant seats per car or total $12$ seats vacant,and there are $11$ persons who dont have car and accompany them. I am stuck here,i cannot count how many ways they can travel by these cars.The answer given in the book is $\frac{11!4!}{(3!)^42!}$

Add the empty seat as a $12$-th passenger. Then there are

$$ \binom{12}{3,3,3,3}=\frac{12!}{3!^4} $$

ways to distribute the $12$ passengers over the four cars. Why they chose to write this in a more complicated way, I don't know.