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jaibean1202
18.02.2020 •
Mathematics
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?
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Ответ:
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:![^9P_{3}\times ^6P_{3}\times ^3P_{3}=504\times120\times6=362880](/tpl/images/0513/7033/0054d.png)
Thus, the number of different ways to arrange the 9 cars is 362,880.
Ответ:
(hope it helps you)