The Pack-U-Up Moving Company uses several different size boxes,but the boxes all have the same meaurements on the top andbottom so they'll stack neatly on top of one another.The only differences between the boxes is their heights: some are three feet high, some are two feet high, and some are one foot high. If the moving company made stacks three boxes high, how many different stacks could be made?
Note that this stack of boxes on the left...
3 is the same as
3
2
3the stack of boxes on the right
2
3
Thanks
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bbc
bbb
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Is that it?
To determine the number of different stacks that can be made, we need to consider the number of choices for each level of the stack.
Let's start with the bottom level of the stack. Since the boxes can be stacked on top of one another, there are three choices for the bottom box: one foot high, two feet high, or three feet high.
For the second level, we also have three choices, since any box can be placed on top of the box chosen for the bottom level.
Finally, for the top level, we still have three choices.
To find the number of different stacks, we multiply the number of choices at each level:
3 (choices for the bottom) × 3 (choices for the middle) × 3 (choices for the top) = 27
Therefore, there are 27 different stacks that can be made if the moving company stacks the boxes three high, considering the given box heights.