"Tommy has 16 toy trucks. How many different arrays can he make with all the trucks?What are the arrays?"
5 Arrays
1x16
16x1
2x8
8x2
4x4
1x16
16x1
2x8
8x2
4x4
1x16
2x8
4x4
8x2
16x1
dont give him this! hes just making you do his hw...
he has 5 arrays
16
To find out how many different arrays Tommy can make with his 16 toy trucks, we can break down the problem into smaller steps.
Step 1: Determine the possible number of trucks in each row.
Since Tommy has 16 trucks, he can have any number of trucks in each row from 1 to 16.
Step 2: Determine the number of rows.
To find the number of rows, we need to consider that each array should have at least one row and that the total number of trucks remains the same. So, the number of rows can range from 1 to 16.
Step 3: Calculate the number of different arrays.
To calculate the number of different arrays, we need to count all the possible combinations of trucks in each row. This can be done by multiplying the number of possible trucks in each row by the number of possible rows.
Let's break down the calculation for each possible number of trucks in a row:
1 truck per row:
As there is only 1 truck in each row, Tommy will have 16 rows, and there will only be one possible array.
2 trucks per row:
The total number of rows will be the number of trucks divided by the trucks per row, which is 16/2 = 8. Since the order of trucks within each row matters, the number of different arrays for 2 trucks per row will be 8!.
3 trucks per row:
Similarly, the number of rows will be 16/3 = 5. The number of different arrays for 3 trucks per row will be 5!.
Continue this process for 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16 trucks per row.
After calculating the number of different arrays for each number of trucks per row, we will add up all the results to find the total number of different arrays that Tommy can make with his 16 toy trucks.