17. Two schools A and B organize student teams to participate in a debate competition. School A recommends $3$ male students and $2$ female students, while school B recommends $3$ male students and $4$ female students. The students recommended by both schools participate in training. Since the students' levels are comparable after training, $3$ people are randomly selected from the male students and $3$ people are randomly selected from the female students to form a representative team. (1) Find the probability that at least $1$ student from school A is selected for the representative team. (2) Before a certain competition, $4$ people are randomly selected from the $6$ team members to participate. Let $X$ denote the number of male students participating, find the probability distribution and mathematical expectation of $X$.
17. Two schools A and B organize student teams to participate in a debate competition. School A recommends $3$ male students and $2$ female students, while school B recommends $3$ male students and $4$ female students. The students recommended by both schools participate in training. Since the students' levels are comparable after training, $3$ people are randomly selected from the male students and $3$ people are randomly selected from the female students to form a representative team.\\
(1) Find the probability that at least $1$ student from school A is selected for the representative team.\\
(2) Before a certain competition, $4$ people are randomly selected from the $6$ team members to participate. Let $X$ denote the number of male students participating, find the probability distribution and mathematical expectation of $X$.