Discussion
For a group of 250 candidates, the number of candidates who passed in Physics is 120, in Chemistry is 100 and in Maths is 90. 40 passed in both Physics and Chemistry, 35 in both Physics and Maths, and 30 in both Chemistry and Maths. If only 15 candidates passed in all three subjects, how many candidates failed in all three subjects?
Answer: A
We first find the number of candidates who passed in at least one subject, n(P ∪ C ∪ M).
n(P∪C∪M) = n(P)+n(C)+n(M) - n(P∩C) - n(C∩M) - n(P∩M) + n(P∩C∩M)
= 120 + 100 + 90 - 40 - 30 - 35 + 15
= 310 - 105 + 15 = 205 + 15 = 220.
Number of candidates who passed in at least one subject is 220.
Total candidates = 250.
Number who failed in all three = Total - Passed in at least one = 250 - 220 = 30.
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