Answer:
The number of different ways to arrange the 9 cars is 362,880.
Step-by-step explanation:
There are a total of 9 cars.
These 9 cars are to divided among 3 racing groups.
The condition applied is that there should be 3 cars in each group.
Use permutation to determine the total number of arrangements of the cars.
- For group 1:
There are 9 cars and 3 to be allotted to group 1.
This can happen in ways.
That is, ways.
- For group 2:
There are remaining 6 cars and 3 to be allotted to group 2.
This can happen in ways.
That is, ways.
- For group 3:
There are remaining 3 cars and 3 to be allotted to group 3.
This can happen in ways.
That is, ways.
The total number of ways to arrange the 9 cars is:
Thus, the number of different ways to arrange the 9 cars is 362,880.