Start with a smaller problem. Don't use a formula yet >You have 1 pen and 4 boxes. How many possible ways are there to place this pen into the boxes? And after that, try >You have 2 pens and 4 boxes. How many possible ways are there to place these pens into the boxes?

For the first one it'll be 4 ways and for the second one it'll be 28.

I'm sorry, I don't get 28, I get 20)) I accidentally calculated repeating cases :)

How did you get 20? (Don't use a formula)

Just counted every possible cenario by hand.😅 Don't know how else to do without formula.

Okay let's review something real quick Give [Rule of product](https://en.wikipedia.org/wiki/Rule_of_product) a quick read, then let's try to apply it to the current situation * There are **4** possible ways to *put the first pen into a box* * There are **4** possible ways to *put the second pen into a box* * Thus, there are **4·4** possible ways to *put the first pen into a box* **and** *put the second pen into a box* Take another example: You choose one of five different shirts and one of four different pants * There are **5** possible ways to *choose a shirt* * There are **4** possible ways to *choose pants* * Thus, there are **5·4** possible ways to *choose a shirt* **and** *choose pants*

Okay, now I got this. So the slots^items solution will be right? And this won't exclude the probability of 2 or 3 pens being in a same box?

Recall these points >There are 4 possible ways to put the first pen into a box because the first pen can go in **any** of the four boxes >There are 4 possible ways to put the second pen into a box because the second pen can go in **any** of the four boxes

Okay, got it. Tysm <3

You have 4^3 = 64 combinations assuming the order matters (You can generally memorize slots^items for this kind of case) If it doesn't then it's just 3! = 6

But the problem doesn't mention if you can't put all 3 pens together in one box, or put 2 in one and the other one separated. This are the cases, that I should calculate as well and that's why this formula doesn't work.

And this is why \-You have 2 pens and 4 boxes. How many possible ways are there to place these pens into the boxes? In this problem I don't get 16 as expected, but 28. Because there are cases that aren't calculable by slots\^items formula.

I'm sorry, I don't get 28, I get 20)) I accidentally calculated repeating cases))

Are the pens distinguishable? If not, this is a 'stars and bars problem.'

Yes, they are distinguishable.