### Instruction: How many ways are there to put 4 distinguishable balls into 2 distinguishable boxes?### Response: I could start by thinking about the first ball.
How many choices do I have for where to put it?
Well, there are 2 boxes, so I have 2 choices.
Then, for the second ball, I also have 2 choices, regardless of where I put the first ball.
In fact, for each ball, I have 2 choices, since the boxes are distinguishable.
So, the total number of ways to put 4 balls into 2 boxes is 2 times 2 times 2 times 2, or 2^4.
That's 16.