need help please

Question

A survey of 500 farmers showed that of the farmers, 128 grew only wheat, 111 grew only corn, 88 grew only oats, 202 grew wheat, 57 grew wheat and corn, 50 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.

Answer 1

draw a Venn diagram with 3 overlapping circles inside a rectangle

the Universe = 500

for Wheat, Oats and Corn only

circle W = 128

circle O = 111

circle C = 88

those are the non-overlapping parts of the 3 circles. that sums to 327

the full W circle = 202, 202-128=74 overlaps with O and C

full C circle = 156, 156-111 = 45 overlaps with W and C

full O circle = 192

overlap of W with O = 50

overlap of W with C = 57

overlap of O with C = 64

how many grew

a) at least 1 of the 3 432

b) all 3 33

c) none of the 3 68

d) exactly 2 of the 3 72