A group of n friends go to the gym together, and while they are playing basketball, they leave their bags against the nearby wall. an evildoer comes, takes the student id cards from the bags, randomly rearranges them, and places them back in the bags, one id card per bag. (a) what is the probability that no one receives his or her own id card back? hint: use the inclusion-exclusion principle. (b) what is the limit of this proability as n â â? hint: e x = â â k=0 x k k! .