Answer to Question #36848 in Combinatorics | Number Theory for GIDEON ESEKON

Question

Out of 250 students who failed in an examination, it was revealed that 128 failed in mathematics, 87 failed in physics and 134 failed in chemistry. 31 failed in mathematics and physics, 54 failed in chemistry and mathematics, 30 failed in chemistry and physics. Find how many candidates failed in:
(a) In all the three subjects (7 marks)
(b) In mathematics but not in physics (2 marks)
(c) In chemistry but not in mathematics (2 marks)
(d) In physics but not in chemistry or in mathematics (2 marks)
(e) In chemistry or in mathematics but not in physics (2 marks)
Hint: Use venn diagram to simplify your work.