There are A guys in a room. Each of them selects independently a uniformly random number from the set {1,2,...,n}. It is said that a crash happens if there exist two guys selecting the same number....

There are A guys in a room. Each of them selects independently a uniformly random number from the set {1,2,...,n}. It is said that a crash happens if there exist two guys selecting the same number. Let , where b is some constant that does not change with n. Prove that there is a constant b_0"> , then a crash happens with probability 1 when . Find the value of as well.