what i did was, Total= 50+40+30-exaclty two-2*3
i am not getting it why it is 17?
Make a venn diagram like so (this is seemingly the way that you’re attempting):
Note that the sum must be 100, so it’s easy to see that x + y + z + 3 = 17
Alternatively, you can also use inclusion exclusion like so:
|A \cup B \cup C| = |A| + |B| + |C| - |A \cap B| - |B \cap C| - |C \cap A| + |A \cap B \cap C|
which gives: 100 = 50 + 30 + 40 - (x + 3) - (y + 3) - (z + 3) + 3 hence x + y + z + 3 = 17
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This is also right bc this gives you exactly two = 14. Since the question asks for “at least two” then you must consider the case where a student can own all three too.
So 14 + 3 =17
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ah!, i got it now. Thanks a lot.