The question is, "How many possible ways could you split 24 unique color balls among 3 bins such that these 3 bins gets at least 1 ball?"

I've tried thinking that there were 24! permutations, and for each possibility, I can draw two "lines" in spaces between the balls and split the balls into three groups. That gives me 23C2 choices, and then I use the product rule and multiply these two together.

The problem with this is that each person that it doesn't keep track of the order of the balls.

Then I tried solving case by case but because there are 23C2 cases . . . well, that's quite large to solve by hand.

Please help, I'm so confused! Thank you in advance for your time and explanation!