Birthday Problem in Hashing

Description of Problems Below the birthday problems are described in terms that can be applied to the security of hash functions. Note that the term likely in all cases means with the probability P≥ 1/2. Problem 1: What is the minimum number, k, of students in a classroom such that it is likely that at least one student has a predefined birthday? This problem can be generalized as follows. We have a uniformly distributed random variable with N possible values (between 0 and N-1). What is the minimum number of instances, k, such that it is likely that at least one instance is equal to a predefined value?