Counting(equally sized boxes)

Question
I have a square which consists of i by i equally sized boxes for a total of N = i·i boxes. In how many ways could I randomly thrown n objects or particles into these N boxes? (where n < N and only 1 object fits in each box).


Can anyone please comment if its right or not. Please

statistics said:

Question
I have a square which consists of i by i equally sized boxes for a total of N = i·i boxes. In how many ways could I randomly thrown n objects or particles into these N boxes? (where n < N and only 1 object fits in each box).


Can anyone please comment if its right or not. PleaseView attachment 8543

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Just a comment signifying nothing: One of the things which might stand you in good stead is that doing things n times one at a time [in the same exact way] is the same as doing all n things at the same time (and in the same way).

On to the problem: What you have done is sort of the correct approach in that the answer is a product of n factors, but why are you, for example, dividing 15 by 3. So, let's start over
-The first particle gets N choices
-The second particle has N-1 choices for a total of N*(N-1)
-The third particle has N-2 choices for a total N*(N-1)*(N-2)
-...
The n^th particle has ??? choices for a total of ???

Comment: In sort of an answer to the 'why divide 15 by 3', it appears you may have been trying for some kind of factorial notation in your answer. If so, you didn't get it quite right.