SOLUTION: A survey of 100 students at New England College showed the following: 47 take English. 49 take history. 38 take language. 13 take English and history. 16 take English and lang

Question 1148927: A survey of 100 students at New England College showed the following:
47 take English.
49 take history.
38 take language.
13 take English and history.
16 take English and language.
18 take history and language.
7 take all three.
I've already figured out a-b and e-f. All I need help with is c-d.
(c) Take none of the three?
(d) Take just one of the three?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
the three circles show a common intersection with 7
with English and history it is 13, but 7 are common to all three, so it is 6 with E and H.
with E and L it is 16, but 7 common so it is 9 for E and L
with L and H it is 18 but 7 are common so it is 11 for H and L
That leaves 25 for E, 11 for L, and 25 for H
All the numbers add to 94, so 6 take none of the three
One of the three would be 61.
One has to assume that 2 together must count the fact that it includes all three or the language number doesn't work.
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