Question

Night engineers are going on an energy assessment in 3 cars that hold 2, 3, and 4 passengers,
respectively. In how many ways is it possible to transport the 9 engineers to the
manufacturing facility, using all cars?

Answer 1

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Answer 2

There are 9!/2!7! combinations of 2 engineers for the car that holds 2 passengers.
Having selected a combination of engineers for the car that holds 2 passengers, there are 7!\3!4! combinations of 3 engineers for the car that holds 3 passengers.
Having selected combinations of engineers for the cars that hold 2 and 3 passengers there are only 4 engineers for the car that holds 4 passengers, giving only one combination.
Each combination of 2 engineers can be taken with each of the combinations of 3 engineers. So the total number of ways it is possible to transport the engineers is
\[\frac{9!}{2!7!}\times\frac{7!}{3!4!}\times1=\frac{9\times8\times7\times6\times5}{2\times3\times2}=you\ can\ calculate\]