The birthday problem is a popular problem in probability. The problem involves finding the probability that at least two people have the same birthday in a group of N individuals. An activity scheduling formulation of the problem can be stated as follows: N activities must be scheduled at random during a given scheduling cycle consisting of 200 days. Each activity takes exactly 1 day to complete. The days all have equal likelihood of being selected for any of the activities. Find the probability of a schedule conflict. That is, the probability that two or more activities will be scheduled on the same day (N ≤ 200). Solve for N = 32.