Permutation / Combination Question

Question

I need to figure out the total #of possible Box combinations for the following scenario. Total # must factor in possibilities for all 6 boxes.

 

Box 1 is always empty

Box 2 is either empty or has 1 of 8 possible rocks

Box 3 must have 1 of 4 possible hats

Box 4 is either empty or has 1 ball

Box 5 is either empty or has 1 of 4 possible bricks

Box 6 is either empty or has 1 of 2 possible sticks

 

If possible, please include the formula in case the variables change. Thanks!!!!!!

Answer 1

This is an example of the counting principle.  The total number of combinations is the product of each individual possibility. For example, box one only has one possibility, it is always empty. Box 2 has nine possibilities (either empty or 1 of 8 rocks).  So for all six boxes:

 

1 x 9 x 4 x 2 x 5 x 3 = 1080