Question

In how many ways can you put seven marbles in different colors into four jars? Note that the jars may be empty.

Answer 1

Answer: 16,384

Step-by-step explanation:

The seven marbles have different colours, so we can differentiate them.

Now, suppose that for each marble we have a selection, where the selection is in which jar we put it.

For the first marble, we have 4 options ( we have 4 jars)

For the second marble, we have 4 options.

Same for the third, for the fourth, etc.

Now, the total number of combinations is equal to the product of the number of options for each selection.

We have 7 selections and 4 options for each selection, then the total number of combinations is:

C = 4^7 = 16,384