It is certainly a silly question.
When we store $n$ students in $N$ different day, we say the following for the first student there is $N$ different choices, for the second $N-1$, etc. So that there is $$N\cdot (N-1)\cdots(N-n+1)$$ possibilities.
But I never really understanding why we do a multiplication.
For exemple let's say we have $2$ students Bob and Lea and $3$ days. For Bob there is $3$ choices so that for Lea there is $2$ choices. And then $3+2=5$ choices and the "correct" answer is $3\times 2=6.$
I cannot think where I am wrong.