In a large university, 60% of students play sports, 30% are involved in the arts, and 10% participate in neither activity. Among the sport-playing students, 70% play team sports, and 30% play individual sports. Additionally, 40% of the art-involved students are focused on visual arts, and 60% on performing arts. If a random sample of 200 students is taken from the university, what is the probability that exactly 84 students play team sports, 36 play individual sports, 48 are involved in performing arts, 24 in visual arts, and 8 students participate in neither sports nor arts?

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