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wilderness
- Master | Next Rank: 500 Posts
- Posts: 102
- Joined: Sat Mar 15, 2008 4:03 am
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In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
13
10
9
8
7
I am trying to solve this as part of the set problem using
n(A u B u C) = n(A) + n(B) + n(C) – n(A n B) – n(A n C) – n(B n C) + n(A n B n C)
and assuming that { n(A n B) + n(A n C) + n(B n C) } - n(A n B n C) is my answer.
So 68 = 25 + 25 + 34 - { n(A n B) + n(A n C) + n(B n C) - n(A n B n C) }
Answer : 16.
What is wrong with my approach ? Why can I not do it in the manner I am doing. I have a feeling that I am making a grave mistake because I am not even using the value that 3 people are in all 3 courses. But what is the problem.
Thanks
13
10
9
8
7
I am trying to solve this as part of the set problem using
n(A u B u C) = n(A) + n(B) + n(C) – n(A n B) – n(A n C) – n(B n C) + n(A n B n C)
and assuming that { n(A n B) + n(A n C) + n(B n C) } - n(A n B n C) is my answer.
So 68 = 25 + 25 + 34 - { n(A n B) + n(A n C) + n(B n C) - n(A n B n C) }
Answer : 16.
What is wrong with my approach ? Why can I not do it in the manner I am doing. I have a feeling that I am making a grave mistake because I am not even using the value that 3 people are in all 3 courses. But what is the problem.
Thanks
