Nine cars (3 Pontiacs [labeled 1-3], 4 Fords [labeled 4-7], and 2 Chevrolet's [labeled 8-9]) are divided into 3 groups for car racing. each group consistes of 3 cars, and they are allocated to 3 tracks (1-3), respectively.
1. How many different ways can you arrange the 9 cars?

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.

       There are 9 cars and 3 to be allotted to group 1.

       This can happen in ways.

        That is, ways.

       There are remaining 6 cars and 3 to be allotted to group 2.

       This can happen in ways.

        That is, ways.

       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.

correct answers below: