There are 120 students at University College taking the introductoryJava programming class. The students have access to the followingcomputers:80 students have access to a PC running Microsoft's Windows operating system.40 students have access to a computer running the Apple operating system.10 students have access to a computer running the Linux operating system.30 students have access to a computer running the Apple or Windows operating system.7 students have access to a computer running the Windows or Linux operating system.5 students have access to a computer running the Apple or Linux operating system.How many have access to computers running all three operating systems?The solution, using the Inclusion-Exclusion principle for 3 sets wikipedia link, is 32. However, how can it be 32 when the number of students who have access to Linux is only 10? 
What's wrong with this problem (Inclusion-Exclusion principle)
discrete mathematics