There are n students in this department, and both Mr. Li and Mr. Zhang send messages to K students at random, which will lead to this situation. Some students only received news from Mr. Zhang, some students only received news from Mr. Li, some students received news from both Mr. Zhang and Mr. Li, and some students received neither news from Mr. Zhang nor news from Mr. Li.

X in the title is the number of students who only received the information from Teacher Zhang plus the number of students who only received the information from Teacher Li, plus the number of students who received the information from both Teacher Zhang and Teacher Li. And there must be many values of x, the minimum value of x is k, and the maximum value is 2k (2k; N), each value of x corresponds to a probability, and the second question requires that among all values of x, when x takes what value, its corresponding probability is the largest.