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?