Seven balls labeled with number 1 to 7 are distributed randomly among seven boxes also labeled with number 1 to 7. And each box can contain at most 1 ball. What is the probability that exactly 2 balls go to boxes with the same number?
It seems that we should fix the 2 correct boxes first, and consider the remaining 5 boxes with inclusion-exclusion principle. But I am not sure how to apply the principle in this situation, what event we should denote here. Can anyone explain it for me?