Puzzle #69: Majors

A university created a sample containing information about 100 of its students.

1) There are 30 Arts majors, 50 Business majors, and 40 Computing majors.
2) 6 students are majoring in Arts and Business, 8 in Arts and Computing, and 10 in Business and Computing. They might be majoring in more.
3) 25 students are majoring in Computing only.

How many fit into each of the eight possible combinations of the three majors (including none)?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, October 1, 2014 at noon Pacific Time. I will post the answer shortly after.