I got the following question: how many options we have to divide N distinct objects into M identical cells when the order matter?
to be honest, Im a bit baffeld about how "order" matter effect the question, I believe its the first time I got a combinatoric question where there was importance to the order
I read a bit about dividing distinct objects into identical cells ( we didnt learn in class stirling number), and Im not sure how I should think about adjusting to the fact order matter
I found this: How many options do we have to divide $k$ balls to $n$ cells (2 conditions)
where he kind of talk about the same question (the bouns) but I cant understand how he figured out the equation
First of all , your question and the question in given link are different from each other.Your question is asking for distinct object in $\color{blue}{\text{identical}}$ boxes where the orders of objects in each boxes matters , but the question in given link is asking for distinct object in $\color{blue}{\text{distinct}}$ boxes where the orders of objects in each boxes matters.
As far as i understood , you are not much familiar with combinatorics (because you say that you do not know Stirling Numbers), but your question requires alittle bit being familiar with combinatorics. I am putting here two links that solve your original question , i hope those can help you when you learn much things about combinatorics :
First Link
Second Link
When we comes to the solution in given link , i think you must have heard about combination with repetition before. Think the question firstly as if it is a problem about distributing identical objects into distinct boxes.It is one of the classical problem of stars and bars method. After you find the solution , convert the identical object into distinct. You can make this convertion by putting an distinct object into (or over) each of the identical objects , and this process can be done by $k!$ ways.