SOLUTION: One hundred twenty people seated at different tables in a Mexican food restaurant were asked if their party had ordered any of the following items: enchiladas, chili con queso or q

Question 1132437: One hundred twenty people seated at different tables in a Mexican food restaurant were asked if their party had ordered any of the following items: enchiladas, chili con queso or quesadillas. 21 people had ordered none of these items; No one ordered only chili con queso; 5 ordered only quesadillas; 11 people had ordered all three of these items; 29 people had ordered chili con queso or quesadillas but did not order enchiladas; 79 people had ordered at least two of these items; 13 people had ordered enchiladas and quesadillas but had not ordered chili con queso; 26 people had ordered only enchiladas and chili con queso.
What is the probability of choosing two persons that ordered only enchiladas?
Answer by greenestamps(13206) (Show Source): You can put this solution on YOUR website!

The way I read the given information, it is inconsistent, making it impossible to solve the problem.

We need to determine the number of people who ordered each combination of the 3 items, enchiladas (E), chili con queso (C), and quesadillas (Q). The possible combinations are {none, E, C, Q, EC, EQ, CQ, EQC}.

(1) 21 ordered none: none = 21
(2) no one ordered only C: C = 0
(3) 5 ordered only Q: Q = 5
(4) 11 ordered all three: EQC = 11
(5) 29 ordered C or Q but not E: C+Q+CQ = 0+5+CQ = 29 --> CQ = 24
(6) 79 ordered either two or all three items: EC+EQ+CQ+EQC = 79 (we'll come back to this)
(7) 13 ordered E and Q but not C: EQ = 13
(8) 26 ordered only E and C: EC = 26

Now going back to (6), we have EC+EQ+CQ+EQC = 79 --> 26+13+CQ+11 = 79 --> CQ = 29

But (5) says CQ is 24 and (8) says CQ is 29.
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