Results 1 to 3 of 3

Math Help - Inclusion-exclusion or difference rule for this problem?

  1. #1
    Newbie
    Joined
    Jul 2010
    Posts
    5

    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:

    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?
    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.


    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?
    Last edited by Hiram; May 7th 2011 at 09:35 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member HappyJoe's Avatar
    Joined
    Sep 2010
    From
    Denmark
    Posts
    234
    If the students are labelled, and you are told the labels of the students who did well in test A, and the labels of those who did well in test B and likewise for test C, then your method of solving the problem is all good.

    If you didn't know which student had done well on which test among A, B and C, then using the inclusion-exclusion principle would be the way to go.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2010
    Posts
    5
    Awesome! Thanks heaps for that HappyJoe. That was exactly the thing I was curious about.

    And for the record, The inclusion-exclusion principle was what I used, for the exact reason you said.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Counting, Inclusion-Exclusion Rule
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 11th 2011, 08:17 PM
  2. A tough Inclusion-Exclusion problem..or...something else
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: July 16th 2010, 05:51 PM
  3. Inclusion - Exclusion Problem
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 14th 2010, 11:06 PM
  4. problem on inclusion exclusion
    Posted in the Discrete Math Forum
    Replies: 10
    Last Post: November 23rd 2009, 01:10 AM
  5. help with inclusion/exclusion problem
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: October 12th 2009, 05:41 PM

Search Tags


/mathhelpforum @mathhelpforum