Assume we have $n$ children and we want to distribute $ n $ packages, each package with a name of one children (and they have different names). I want to count for some $ 1\leq j \leq n $ in how many ways can we distribute the packages, such that $ j $ children would get the right package with their name on it, and the rest $ n-j $ children would get the wrong package.

Im not sure how to do it. Thanks in advnace.