A. Each one of n persons, indexed by 1,2,…,n , has a clean hat and throws it into a box. The persons then pick hats from the box, at random. Every assignment of the hats to the persons is equally likely. In an equivalent model, each person picks a hat, one at a time, in the order of their index, with each one of the remaining hats being equally likely to be picked. Find the probability of the following events. 1. Every person gets his or her own hat back.2. Each one of persons 1,…,m gets his or her own hat back, where 1≤m≤n.3. Each one of persons 1,…,m gets back a hat belonging to one of the last m persons (persons n−m+1,…,n), where 1≤m≤n.