Say you have 5 identical balls. You want to put them into 4 different boxes. What is the total number of ways the balls can be arranged?
For example, you could have all 5 balls in one box. You could have 3 balls in one box and 2 balls in another, etc.
The Attempt at a Solution
Since the balls are identical, order doesn't matter and this is a combination. So I drew it out, and figured out the correct number of ways - basically by doing a tree diagram.
But what I'm actually trying to figure out is what the equation looks like. I want to generalize it so that it works for m boxes and n balls, so I thought I'd make up a more concrete example to help me.