Inclusion-exclusion or difference rule for this problem?
Hi guys, I have a problem, and I'm not sure which method I should be using. I didn't want to get too far into the work before I realise that I've chosen the wrong method.
The problem is:
I'm pretty sure I should be using inclusion-exclusion for the problem, but as I'm not very good with mathematics, I'm not sure. Any help you guys could provide would be great.
in a class, three tests were given. out of ... students in the class:
... did well on test A
... did well on test B
... did well on test C
... did well on tests A and B
... did well on tests A and C
... did well on tests B and C
... did well on all three tests
How many did not do well on any test?
Edit: After playing around with this, I've tried using the difference rule and I've gotten an answer that's correct to me.
Out of ten students (labelled 1-10):
4 did well on test A (1, 2, 3, 6)
4 did well on test B (2, 3, 6, 8)
3 did well on test C (6, 8, 9)
Using those values, just by looking at it I can see that students 4, 5, 7 and 10 didn't do well on any test.
Let T = all the students, let A be students who did well on test A, B be students who did well on B, and C be students who did well on test C, that you can get the answer by doing | T | - | A U B U C | (the difference rule) which gives four, which is the correct answer from above.
So I think I'm doing it correctly, but I can't understand the relevance of all other data? e.g. students who did well on A and B, B and C, or on all three tests? Is there something I'm missing, or are they unnecessary for answering this question?