The class registration of 120 students are analyzed. it is found that 30 of the students don't take any of applied mechanics, chemistry, or computers. 15 of them take only applied mechanics.25 of them take chemistry and computers but not applied mechanics.20 of them take applied mechanics and computers but not chemistry.10 of them take all three of applied mechanics, chemistry and computers. a total of 45 of them take chemistry. 5 of them take only chemistry.
a) how many of the students take applied mechanics and chemistry but not computers?
b) how many of the students take only computers?
c) what is the total number of students taking computers?
d) if a student is chosen at random from those who take neither chemistry nor computers, what is the probability that he or she doesn't take applied mechanics either?
e) if one of the students who take at least two of the three courses is chosen at random, what is the probability that he or she takes all the three courses?