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A survey of 500 farmers showed that of the​ farmers, 121 grew only​ wheat, 108 grew only​ corn, 92 grew only​ oats, 195 grew​ wheat, 59 grew wheat and​ corn, 48 grew wheat and​ oats, and 176 grew corn. Determine the number of farmers who ​a) grew at least one of the​ three, ​b) grew all​ three, ​c) did not grow any of the​ three, and ​d) grew exactly two of the three.

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Answer:

The farmers in regions II, IV, and VI had exactly two of the three Summing the numbers in these regions 25 + 15 + 10 we find the that 50 farmers grew exactly two of the three.