Answer to Question #35404 in Combinatorics | Number Theory for Pankaj

out of 250 candidates who failed in an examination, it was revealed that 128 failed in mathematics, 87 in physics and 134 in aggregate, 31 failed in mathematics and in physics 54 failed in the aggregate and in mathematics, 30 failed in the aggregate and in physics. find how many candidates failed.
1 in all the three subjects. 2. in mathematics but not in physics. 3. in the aggregate but not in mathematics 4. in physics but not in the aggregate or in mathematics 5. in the aggregate or in mathematics, but not in mathematics