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 the stack of
3 2 boxes on the right
2 3

Just different heights? Or are orders of stacking important?

We do not have a clear indication of what "this stack of boxes" is.

Review your information on combinations and permutations.

A stack of books is

63
inches high. How high is it in feet and inches?

To determine the number of different stacks that can be made, we need to consider the possible arrangements of stacked boxes.

Since the stacks are three boxes high, we can think of each stack as having three levels. Let's label the levels as A, B, and C.

To figure out how many different stacks there could be, we need to determine the number of combinations for each level. Since each level can have boxes of different heights (1 foot, 2 feet, or 3 feet), we can calculate the number of combinations using the multiplication principle.

Level A can have three possible box heights (1 foot, 2 feet, or 3 feet).
Level B can also have three possible box heights.
Level C can have three possible box heights as well.

To find the total number of different stacks, we multiply the number of possible combinations for each level:

3 (options for level A) x 3 (options for level B) x 3 (options for level C) = 27 different stacks.

Therefore, the Pack-U-Up Moving Company could make 27 different stacks when stacking the boxes three high.